reference check from closed facility

Now, before the facility closes, ask the HR department how employment records will be stored, by whom, and what contact to list for future references. They'll know.

Ditto. Also, now, approach any superiors with whom you have a good relationship and ask them if they'll be willing to be references for you in the future and, if so, how can you get in touch with them once the facility is closed. I've worked in the past for facilities that have closed, but have been able to note on employment applications since then that the facility no longer exists, but my previous boss is willing to be contacted about me (and give the contact info).

wouldn't hurt to ask for a letter of reference

You are entitled to a copy of your personel file. I would ask for it now. Make sure it includes copies of your evualations. I would also ask your current supervisor(s) and co-workers for a written referrence now. You will be able to use them even if you lose contact with these people.

Since the facility is closing the administration should have no problems with these requests.

Good luck in your job search.