As a partial answer, a first step was in 2005 when UNHCR adopted (so I don't say copied) the EU notion of subsidiary protection.
In 2004, a need to harmonise the principles of these above-mentioned laws into one instrument
was attempted at a regional level by the European Union (EU) through a binding supranational
legal instrument adopted by EU Member States: the EU Qualification Directive. Then in 2005, a
non-binding EXCOM Conclusion was agreed at the international level by seventy-two states.
This encouraged states to use ‘complementary forms of protection for individuals in need of
international protection who do not meet the refugee definition under the 1951 [Refugee]
Convention or the 1967 Protocol’. [citing]
To be fair to UNHCR, there were discussing these before in
There were probably more steps before they just decided to call these just refugees, so I'm open to accepting a more complete answer.
Another one was probably this public appeal of the High Commissioner:
In the September/October 2008 issue of Foreign Affairs, the UN High
Commissioner for Refugees, Antonio Guterres, reached out to the world’s policy
elites with an appeal. He wrote, “UNHCR confronts a disconnect between
the limited formal mandate of protecting refugees and the immense scope of
forced displacement around the world today” (Guterres 2008:91). He predicted
that climate change, natural disasters, famine, and unstable states would be the
main causes of displacement in the 21st century and asked receiving states to
develop a new “humanitarian protection compact” to meet the needs of those
migrants who are forced from their homes, but are beyond the scope of the 1951
Convention (Guterres 2008:92). As Guterres articulated, the practical reality
of forced migration today is that, increasingly, people around the world are fleeing
generalized violence and natural disaster rather than individualized persecution.
To put it another way, many of the world’s displaced people may look like
refugees or feel like refugees to the average observer, but are not refugees in the
technical sense of the word as it is used in international law. Thus, they may not
be found eligible for refugee protection by the states in which they seek refuge.
[-- quote from R. Hamlin, Let Me Be a Refugee referencing]
The earlier evolution of UNHCR's thinking/position is recounted by Hamlin as:
For its part, the UNHCR has gradually come around to the idea that its mandate
includes advocating for an international complementary protection regime.
Although the Executive Committee has reaffirmed on a number of occasions
that the 1951 Convention is the “foundation” and “cornerstone of the international
refugee protection regime,” in recent years the agency has also taken to
insisting that “the human rights base of the Convention roots it quite directly
in the broader framework of human rights instruments of which it is an integral
part” (UNHCR 2001, 2009). In this way, the UNHCR seems to have adopted
the Goodwin-Gill/McAdam unitary approach to the relationship between
international refugee law and human rights law. Although some states have, historically,
offered protection to people who fell outside the Convention definition
of a refugee for a variety of reasons, by the 1990s the UNHCR began to
push states to offer protection more consistently and expansively. Beginning in
1994, the UNHCR explicitly defined the people within its purview using the
expansive OAU and Cartagena definitions, not the definition from Article 1 of
the Convention (UNHCR 1994). Since 2005, UNHCR has recommended that
states integrate their RSD systems to include complementary protection as part
of one “comprehensive procedure” (UNHCR 2005). [...] the agency maintains the distinction
between refugees and other migrants simply by encouraging an expansion
of the refugee category. It is strategically necessary for the UNHCR to promote
the distinction between categories to avoid being seen as interfering in migration
policymaking, which is closely linked to sovereignty.
An EU document notes that the UNHCR had been using (some version) of their extended definition for quite some time for statistical purposes, with the most recent expansion of scope in 2007:
The numbers refer to the following category of persons as defined by the UNHCR for statistical purposes: 'In UNHCR
statistics, refugees include individuals recognized under the 1951 Convention relating to the Status of Refugees; its
1967 Protocol; the 1969 OAU Convention Governing the Specific Aspects of Refugee Problems in Africa; those recognized
in accordance with the UNHCR Statute; individuals granted complementary forms of protection; or, those enjoying
"temporary protection". Since 2007 the refugee population category also includes people in a refugee-like situation,
most of whom were previously included in the Others of concern group. This sub-category is descriptive in nature and
includes groups of persons who are outside their country or territory of origin and who face protection risks similar to
those of refugees, but for whom refugee status has, for practical or other reasons, not been ascertained.'
In the early 1990s, when the UNHCR had started to issue position statements with some frequency, one of them (EC/1992/SCP/CRP.5) reviewed the "persons of concern to UNHCR who fall outside the 1951 Convention", and after looking at the various forms of protections for them that existed back then, concluded with a call for at least a uniform terminology:
A generalized threat to physical safety or security, external displacement and a temporary protection need are common elements in all these various and different approaches to defining the persons of concern. These would also, presumably, be the basis for delineating the category(ies) of beneficiaries of any new protection framework. As a subsidiary point, it would be useful to have one agreed term to describe persons who cross national borders in need of international protection, but who fall outside the 1951 Convention. They have been variously referred to as OAU/Cartagena-type refugees, externally or internationally displaced persons, persons fleeing danger, victims of violence, humanitarian cases, de facto refugees, B-status cases, and Temporary Protected Status cases.