Short description:
- start foobar2000
- place it in bottom right corner of the screen (btw. docking ability would be a nice option...)
- lock the screen
- log as a different user
- change to lower resolution, change back to default resolution
- log back to account with running foobar

after that foobar moves to fit screen in lower resolution, but it was changes on other profile so shouldn't affect foobar (at least other programs stays where I left them). Could it be fixed?

The screen resolution is a global setting in Windows, it is not separate for individual user accounts.

OK, fine... but why only foobar2k is being affected?

I think that this is the wrong question. I have no idea why only foobar2000 would be affected, since I don't know your setup.

A possible reason why it is affected at all is that lowering the screen resolution would put the foobar2000 window off-screen, but Windows prevents that by moving the window.

Therefore I've wrote in first post steps for comparison. It's possible that there is something wrong with my OS and replies like "works fine with me" would only assure that. However, if it's not only issue with my computer I'd be glad to see an option allowing foobar2k to stick in one position