What country are you in? Definitely if you're in the US or Europe there are plenty of places you can apply for government funding if you're a composer.

Also if the government is funding the concert hall and that funding lets the concert hall put on work by and pay a composer, at what point does it stop being government funding?

> at what point does it stop being government funding?

It's a good question, and I replied to that in another comment.

http://www.playbill.com/article/national-endowment-of-the-ar...

https://www.musicofremembrance.org/news/national-endowment-a...

If you specifically want an example of a grant being awarded to a composer for the purposes of composing a new piece, see here:

https://www.broadwayworld.com/bwwclassical/article/Chicago-P...

"The Chicago Philharmonic Society has been named the recipient of a $10,000 Art Works grant from the National Endowment for the Arts. The award will support a collaboration between The Chicago Philharmonic Society, composer Augusta Read Thomas, and Chicago-based percussion ensemble Third Coast Percussion for the creation and performance of a new work for percussion quartet and orchestra. The premiere will be presented in fall 2017 as part of the Chicago Philharmonic's 2017-2018 symphonic season."

No, but if really I wanted to find one I'd probably start by looking here: https://www.arts.gov/ and then continue looking at smaller and more local arts grants. Also I'm sure that at some point some part of the government has commissioned new music for some project or event, although it's quite possible that that music has never been released on a CD.

But again it's all down to how you draw the line. Are you asking if there are composers on the federal payroll or if a composer has ever won a government grant and uses the money for that grant to pay his rent while continuing to compose?