Don't quit - you will not get unemployment insurance. Why don't you continue to work the reduced hours (whatever hrs. they might give you) while looking for another job? If you do, you *might* be eligible for partial benefits. If you continue to work at reduced hours, most states will see that as no fault of your own and pay a partial benefit. If you quit, you will get nothing.
I would put in a claim for unemployment ins. - it sure can't hurt.
P.S. You really should have started your own new thread. It gets confusing when there is more than one question under a thread. This is the 3rd under this thread.

