It depends on the airport and airline, sometimes they let it go round and round for hours, sometimes like at LGA they pull it and stack it in 10 rows by the last digit of your claim check, some like Delta at ATL or UA at JFL move it into a claim area.

The big risk I see is that somebody may be luggage shopping (I see it quite a few times at LGA, people come in, check out all the bags, and pick out a nice one and run off with it) and if it's there and nobody has claimed it they may walk with it.

I'd ask the airline how they handle it and what your options are.