I rent an apartment in s. fla and the landlord has stopped paying the h.o.a.. I have no lease or written agreement to live here.

Your rights as a tenant are outlined in Fla. Stat. s. 83.40, and following. As to the non-payment of HOA fees, if the HOA moves to foreclose its claim, you will be named as defendant. It is not likely that you would be required to move as result of any judgment in favor of the HOA. However, because you are a tenant-at-will (without a lease) your landlord may give you written notice that comports with s.83.56 which would terminate your tenancy, resulting in you having to vacate the premises.