I don't know who the key players/thinker in this are, but the most common meaning of the term as in use today seems to come from the so-called neo-Schumpeterian economics. They don't exactly predict the end of capitalism (as a result of this), like Schumpeter appears to have done (inspired by Marx). Instead the neo-Schumpeterian reappropriation of the term is that
Schumpeter emphasized creative destruction in which exits are important. Exits may for
instance reflect a process where less efficient firms are displaced by new firms. When firms exit,
resources previously held by the existing firms can be allocated to more productive means elsewhere
in the economy.
I'm guessing resources there include workers.
On a quick search, https://www.jstor.org/stable/23601693 appears to be a fairly highly cited paper in this area, which you may want to read. A lead there:
Creative destruction in a Schumpeterian
sense is most often closely connected to the obsolescence of labour qualifications
which may cause severe problems of mismatch unemployment on the labour markets—the
new qualifications are not sufficiently available, whereas obsolete qualifications abound.
And then they drop a remark about the "Danish model implemented since the 1990s", which I'm guessing refers to what's elsewhere called the "Danish flexicurity model".
They also mention Fourastié at one point, in ref to his 3-sector theory. Fourastié essentially describes the need for services as "endless", so I'm guessing a great absorber of extra workforce. (Quip to Macron here, I guess: cross the road and get a job... as a mirror cleaner.)
Fourastié offers a striking example: in 1700, the cost of producing four square meters of mirrors (as in Versailles’ Hall of Mirrors) represented 40,000 hours of unskilled labor; this cost then dropped to 6,500 hours in 1850, 550 hours in 1900, and only 100 hours in 1950. Manufacturing mirrors has high productivity gains and is thus classified as part of the secondary sector. However, the cost of cleaning a mirror was one hour of unskilled labor under Louis XIV and has remained around this level ever since. Hence, cleaning activity, which exhibits approximately nil productivity gains, is classified in the tertiary sector.
although neo-Schumpeterians phrase this more generally at the sector/industry level:
new industries emerge again and again throughout the history of capitalism,
driving out existing ones or at least considerably changing their relative weights.
Now I don't know where you've read that part, but generally speaking the number of jobs [by which you seem to mean employed persons] is not posited to stay the same if there are frictions in employment, particularly re-training related ones. It's generally accepted that it is rather an intergenerational process, in practice:
A consistent finding in this literature is that new cohorts of workers account for a disproportionate share of the net reallocation of labour. For example, more than half of the transition from agriculture to non-agriculture is accounted for by new cohorts of workers entering the labour market in non-agricultural jobs while older cohorts of workers retire from agricultural work. The literature has typically viewed this finding as evidence that either a lack of human capital or other barriers limit the ability of existing workers to take advantage of opportunities in growing sectors.
So yeah, not only do firms exit, but so do people/workers. Luckily new ones enter, hopefully with better skills, so the market clears in that sense.
Now I'm hardly an expert on [neo-]Schumpeterian models, but on a quick look they don't seem to get into the details of what happens on the labour side, other than assuming that it clears. Their focus is on the "creative destruction" only on the firm side, AFAICT.
However Schumpeter himself did reflect quite a bit on the nature of unemployment:
In his theory of economic development Joseph A. Schumpeter explained cyclical, structural and other types of unemployment as effects of one and the same cause, namely creative destruction. This led him to define unemployment in all its manifestations largely as a frictional phenomenon.
[...] While Schumpeter’s ideas about growth and innovation have been a source of inspiration
for the new paradigm, modern authors rarely, if ever, refer to Schumpeter’s discussion of
unemployment issues. [...]
The kind of unemployment that is essentially associated with business cycles is,
according to Schumpeter (pp. 514-15), related to technical progress. He used the phrase
“technological unemployment” in his Business Cycles (1939) to describe not only the
displacement of workers by machinery (as in  1934, p. 250), but all employment effects of labour reallocation induced by creative destruction through innovations – i.e. by changes in the production functions and by the replacement of old by new firms.
It is the priority of this broad concept of technological unemployment that sets Schumpeter apart from the rest of the economic literature:
Few, if any, economists realize the one major point that the writer wishes to make.
They have a habit of distinguishing between, and contrasting, cyclical and
technological unemployment. But it follows from our model that, basically, cyclical
unemployment is technological unemployment. Technological unemployment… is
of the essence of our process and, linking up as it does with innovation, is cyclical
by nature. (1939, p. 515; italics in the original)
described cyclical technological unemployment as “frictional”, Schumpeter (1939, p. 516) was at
pains to stress that this definition did not indicate any intention to “minimize the importance of
the phenomenon or the sufferings it inflicts”. He argued nevertheless that the primary interest of
workers is in the effects of innovation on their long-run aggregate income “and not in the
incident variations of employment, which is but an element of the mechanism that produces the
changes of the former and can be separately handled by public policy”.
[...] Yet modern modeling techniques do also help to substantiate as well as modify
Schumpeter’s intuitive insights. A case in point is Schumpeter’s assertion of the stationarity of
long-run unemployment. Schumpeter’s unemployment series ( 1951, p. 200) have been extended up to 1990 by Layard, Nickell and Jackman (1991, pp. 3-5). Like
Schumpeter, they conclude that unemployment is untrended over the very long term. Such
empirical evidence has led some authors to regard the absence of long-run effects of the level of
productivity on the steady-state (or “natural”) rate of unemployment as one of the conditions that
any unemployment model should satisfy (Blanchard and Katz 1997, p. 56). It should be pointed
out, however, that Schumpeter did not categorically exclude the possibility that productivity
growth may affect unemployment in the long-run, especially if it comes along with imperfect
competition. For him it was an empirical question, and there is a yet no consensus about the sign
of the long-term correlation between unemployment and productivity (or GDP) growth, although
zero correlation is often found (see e.g. Mortensen 2005).
[...] Schumpeter was aware that the effects of a constant rate of technological
progress on the level of long-run unemployment would be permanent: “[T]echnological
unemployment, even if essentially temporary so far as the effects of any individual act of
mechanization is concerned, may evidently become a permanent phenomenon through being
incessantly recreated” (Schumpeter 1954, p. 944; [...]). However, except for a brief elliptic passage in the “lost chapter” of 1911, he did not
discuss the effects of a faster rate of technological progress on long-run unemployment (that is, he did not compare different steady states).
So, it's a little complicated. Basically Schumpeter mostly considered constant technological progress, and this seems to have led him to conclude that unemployment would [most likely] be stationary, in the long run. But he also seems to have entertained the possibility it might not be so under some slightly different assumptions that he didn't pursue much.
One thing to note here is that last quote is based on his 1946 works, by and large. It's quite possible that by then he kinda abandoned his predictions from his (most popular) 1942 book, which regarded capitalism as possibly doomed. He was also an immigrant to the US and during the war official views of the USSR were quite softened in the US, but afterwards socialism become less fashionable. (He was even investigated by the FBI, albeit suspected of Nazi sympathies, before the war. Possibly that might have left an impression on him, wrt. the Overton window.)
This more of an aside, but his 1942 wasn't "all for naught" as a prediction method, in particular his views that democracy could undermine capitalism because...
In several articles he wrote during the 1970s and early 1980s Paul A. Samuelson reformulated
the prediction that Joseph A. Schumpeter, his teacher at Harvard, had made in Capitalism,
Socialism and Democracy (1942). Although Samuelson’s views during this period evolved,
sometimes in contradictory ways, the core of his argument remained unaltered. Schumpeter’s
argument can be summarized as follows. First, if certain “observable tendencies” prevailed,
capitalism would succumb due to forces engendered by its own success –“bureaucratization”
of businessmen, a generalized hostility to business and the antagonism of intellectuals– and
socialism would replace it. Second, democracy would survive. Basically, the capitalist
democratic system would be replaced by a socialist democratic system.
Samuelson’s reformulation of Schumpeter consisted in replacing: “capitalism” with the
mixed-economy system prevailing in most advanced Western economies, and “socialism”
with populism. The former would not collapse due to its success in delivering sustained GDP
per capita growth but due to its failure in providing the levels of equality in income and
wealth voters demanded. Capitalist democracy would be replaced by populist democracy.
Samuelson considered the latter system characteristic of the Southern Cone countries and
identified Argentina as the one in which it had reached its fullest development and its effects
felt most intensely.
[...] At the time, Samuelson also believed the advanced Western economies could follow the same path as Argentina. The Reagan and Thatcher revolution proved him wrong. However, the emergence of populism in Europe and the US in recent years makes his reformulation of Capitalism, Socialism and Democracy seem more plausible.
[...] Samuelson believed that stagflation was “intrinsic” to the mixed economy system. He was convinced that slower
growth lied ahead due for Western economies due to higher energy prices, increased laziness
and slower innovation (Samuelson, 1980, pp.71-74). Even in a non-zero sum game, Von
Neumann and Morgenstern’s basic theorem still applied: in a democracy, the poorer 51%
would use the state “to gang up” on the richest 49%. [...]
The same gasoline that classical economists thought ran the laissez faire
system, namely self-interest, will in the context of democracy lead to use of
the state to achieve the interest of particular groups. It is a theorem of von
Neumann’s theory of games that this should be the case. Long before Marx,
John Adams and Thomas Macaulay warned that giving votes to all would
mean that the poorest 51% of the population would use their power to reduce
the affluence of the richest 49% (1981b, p.43)… Social equilibrium a la
Queen Victoria or Calvin Coolidge is unstable. If all groups but one adhere to
its modes of behavior, then it definitely pays the remaining persons to form a
collusion and use the state to depart from the laissez faire beloved by Ludwig
von Mises and Fredric Bastiat (1980, p.70).
It's also interesting to know why Schumpeter didn't think about this. Essentially it's because he didn't think/see inequality would rise in any significant fashion, as a result of capitalism.
By focusing solely on inequality, Samuelson distanced himself from Schumpeter, whose
argument about the demise of capitalism was “by no means wholly economic” (Schumpeter,
1942, p.384). Schumpeter had not considered inequality as a key factor that would drive a
society to embrace socialism because he saw no reason to believe that “the distribution of
incomes or the dispersion about our average would in 1978 be significantly different from
what it was in 1928” (ibid., pp.65-66) However, he [Schumpeter] recognized that fostering “the association
of inequality of any kind with ‘injustice’” was an important “element in the psychic pattern of
the unsuccessful and in the arsenal of the politician who uses him” (ibid., p.254).