It's not crap
It's not crap: a lease is an agreement between a landlord and tenant, not the property and tenant. Normally a landlord will continue to honor a lease. But oftentimes landlords become greedy and cancel leases at their discretion. Lately Florida has been experiencing a sharp boom in the real estate market, driving rent up tremendously.
There are no laws that force a new landlord to honor an old lease. In fact, the new landlord has to draft another lease for the tenant to sign. Where landlord and tenant laws are concerned, Florida needs to revise its laws.
However, there are certain laws which protect the tenant, even if he doesn't have a lease. Any policy changes, rent increases, or other rules by a landlord requires a notice of at least 15 days before the next rent becomes due, on a month-to-month tenancy. Rent increases require at least 30 days notice before the next rent is due.
Florida Statutes: Chapter 83, Part II - Residential Tenancy