David,
As Glen pointed out, FL law incumbers all unpaid assessment debts on the buyer and then it's up to the buyer to go after the previous owner (vs. the Association doing it).
Here are links to the applicable law:
FL 720.3085 applicable to property in Homeowner Associations.
FL 718.116 applicable to property in Condominium Associations.
Here is the language in those statutes (which is effectively the same for both except for substituting parcel owner for unit owner) [emphasis added]:
A unit owner, regardless of how his or her title has been acquired, including by purchase at a foreclosure sale or by deed in lieu of foreclosure, is liable for all assessments which come due while he or she is the unit owner.
Additionally, a unit owner is jointly and severally liable with the previous owner for all unpaid assessments that came due up to the time of transfer of title. This liability is without prejudice to any right the owner may have to recover from the previous owner the amounts paid by the owner.