My daughter signed a one year lease with a roommate in August 2009 and in December they were served papers from a foreclosure atty that the property is in foreclosure procedures. Her roommate decided she wasn't throwing good money after bad and moved out this week, Jan 2010. Are they required by law to continue to pay rent even though the mortgage payment is not being made. We found out that the landlord has three other properties also under foreclsoure. Can he take them to court or file a judgement against them?

Yes, just because he is not paying his bills, has no bearing on their contract.

Yes they have to pay until the properly is formally foreclosed on and sold. Once it is sold, the new owner may want to rent it , or they may want them out.

The landlord in Florida does not even have to try and find a new tenant.
He may sue them for any unpaid rents, and his foreclosure status is no defense.

So they need to just keep living their until it is foreclosed.

You should be considering sueing the room mate since your daughter must now pay the entire rent. Both signing means one or the other or both must pay.