The present owner still remains the owner until the foreclosure is completed. Until then, this individual owns the property and is entitled to receive the rent payments.
The fact that you do not have a lease agreement does not excuse you from your financial obligation to the owner. To not pay may the rent may cause you future problems.
Just because your lease ended doesn't mean you can do whatever you want.
Florida landlord tenant law says that even if your written agreement comes to an end you are still technically obligated to pay rent because leases in Florida are still valid and convert to whatever your payment arrangement is i.e. week to week or month to month. Now your landlord can put a notice on the front door to make you pay but you can take him to court and tell the judge why you are not paying. The concern of course is for your deposit and any payment for rent that you might get evicted for after paying.
Some of the banks are doing a cash for keys - to get tenants and owners out of the house in as reasonable as necessary by giving the person $1000 to $2000 to move-out quickly. This gets rid of some of the inconvenience of it all.
I have attached an article about Fannie Mae working with tenants even through foreclosure and honoring leases etc. I hope this helps and good-luck
Sure property owner happy resolve any issues with you.