According to Florida section 83.806 (6) (which the link in the question amends)
Before any sale or other disposition of personal property pursuant to this section, the tenant may pay the amount necessary to satisfy the lien and the reasonable expenses incurred under this section and thereby redeem the personal property. Upon receipt of such payment, the owner shall return the property to the tenant and thereafter shall have no liability to any person with respect to such personal property. If the tenant fails to redeem the personal property or satisfy the lien, including reasonable expenses, he or she will be deemed to have unjustifiably abandoned the self-service storage facility or self-contained storage unit, and the owner may resume possession of the premises for himself or herself.
Thus the owner may pay-up and stop the sale at any time before the sale occurs. There is nothing in the law preventing the former owner from bidding in person or via an agent, at such a sale. But it is hard for me to see why this route would be taken rather than simply paying the back rent due.