The Example of the Taiwan Power Company
Interestingly, when SOE do exist, they are usually placed under the
ownership of the executive. For example, Taiwan's national power
provider, Taiwan Power Company, is a subsidiary of Ministry of
Economic Affair.
This assertion isn't quite right.
The executive doesn't "own" state-owned enterprises, even if it may control those enterprises. Likewise, describing an entity like the "Taiwan Power Company" as a "subsidiary of the Ministry of Economic Affairs", when really what it does is appoint the company's top officials and supervise them, is misleading.
The profits of the enterprise, if any, go to the state, not to a particular agency's budget for its own purely discretionary use. It can't sell the company without legislative approval either, and if it did sell the company, the proceeds of the sale wouldn't be limited to one branch of government, let alone to use by the particular agency that supervises the managers of the SOE.
The legislature has power to set policies regarding the company and to adopt budgets determining where the economic proceeds of the company go.
Also, in Taiwan, distinguishing different branches of the government is a bit complicated in this semi-Presidential system too, and partisan division between the executive branch and the unicameral legislature has been the exception rather than the rule there:
The government is divided into five branches (Yuan): the Executive
Yuan (cabinet), the Legislative Yuan (Congress or Parliament), the
Judicial Yuan, the Control Yuan (audit agency), and the Examination
Yuan (civil service examination agency).
The head of state and commander-in-chief of the armed forces is the
president, who is elected by popular vote for a maximum of 2 four-year
terms on the same ticket as the vice-president. The president appoints
the members of the Executive Yuan as their cabinet, including a
premier, who is officially the President of the Executive Yuan;
members are responsible for policy and administration. . . .
The premier is selected by the president without the need for approval
from the legislature, but the legislature can pass laws without regard
for the president, as neither he nor the Premier wields veto power.
Thus, there is little incentive for the president and the legislature
to negotiate on legislation if they are of opposing parties. After the
election of the pan-Green's Chen Shui-bian as president in 2000,
legislation repeatedly stalled because of deadlock with the
Legislative Yuan, which was controlled by a pan-Blue majority.
Historically, the ROC has been dominated by strongman single party
politics. This legacy has resulted in executive powers currently being
concentrated in the office of the president rather than the premier,
even though the constitution does not explicitly state the extent of
the president's executive power.
In General
Generally speaking, state owned enterprises as the name implies are owned by the state.
The executive and legislature are simply different parts of the management team of the entity that is the state. They aren't really entities in their own right. Moreover, in parliamentary systems, the executive and legislative branches are in any case, basically fused.
This said, there are some fairly trivial enterprises owned by the state that are managed by a government's legislative branch to the exclusion of the executive branch.
For example, in the United States, the Library of Congress and the Capitol building gift shop are enterprises run by Congress rather than being managed by the President or his appointees, for reasons that are mostly historical accidents or are just expedient.
The U.S. and many other countries also have "independent agencies" which are formally part of the executive branch, but are run by boards of directors or individual directors who are appointed by legislators and/or the executive branch and/or voters in an election, but do not report to them directly.
AMTRAK, the U.S. Postal Service, the Tennessee Valley Authority, the Corporation for Public Broadcasting, many state universities and colleges, and many special districts (e.g. water boards and cemetery boards) operate in this fashion.
While it is not an enterprise exactly, in most U.S. states, the state auditor is appointed by the legislature to the exclusion of the executive branch, because this official's job is to investigate the executive branch.