Do they? I don't.
In fact when I was last employed (I'm now freelance, or at least trying to be freelance) I very much did not work on my OSS project, or use it in client work, because while I had verbal assurances that the company would not assert their rights, the contract I signed included an IP clause that was a little too broad for my liking.
As to the OP, It would be nice if I could figure out a way to make my OSS project earn enough to cover my rent. I would be really happy if I could get it to pay its own rent - hosting the project's home page is not $free.
(Obligatory spam of the project's home URL: https://scrawl-v8.rikweb.org.uk/ )