It is possible.
Do you put poison out to kill them? Despite what the packages say they do not go outside to look for water and die. They often die in the walls.

Could be a spot where they fall in a crevice and cannot get out.

We've had the Exact same problem in the Exact same area (between bedroom/closet/bath) with about the Exact same sporadic frequency. We've searched high and low outside & in attic trying to figure out what it might be or how it might get in. We don't hear running, very little scratching, but more of a flop-flop. We think it could be a field mouse or a bat/bird that got in but can't get out. We've gotten a few cats outside & now it's been a long time since the last occurrence.

In our old house, decades ago, we were told to put out Exlax tablets in the attic so the critter would die w/o the smell. It seemed to work then, but I haven't tried it in years. Good luck, I empathize with your situation.

look for the opening the critter is getting access into your home from.
plumbing penetrations would be the place I would start.
check under sink..open plumbing access and seal pipes
penetrations, under house (if on piers or basement crawlspace) and attic @ pipes.
People have told me that mice/frogs/etc came in the weepholes in the brick..but usually we found several areas where they could get inside...
Mice can squeeze into amazingly small openings.

best of luck....LOL @ the exlax...

Thanks for all of the info. We live in a condo, and after doing a little investigating it turns out that our association places a rat bait box outside of the patio next door. I'm wondering if they're taking the bait then finding a crawl space that leads directly into our bedroom. Maybe I can get them to add the exlax into the bait box... :)