Legal Question in Landlord & Tenant Law in Florida

You can take possession of the abandoned property and re-rent it. You can sue for the rental not paid. If you have a security deposit, you can impose a lien properly on those funds.

You can sue them for the rent owed and future rent on the lease up until the point that you re-lease the premises, or you can elect to wait until the lease expires and sue then, but the premises can't be rented if you do that. Most will choose option 1, because you want to re-rent the place as fast as possible to keep the rent coming in (no kidding, right?). You should probably send the 3 day eviction notice and post it to the door and document that you did it. If you do that and wait 10 days, you can legally take possession if they don't come back to get their stuff. You might want to consult a local attorney before you do anything.