trapped in Florida homestead exemptions on tax lien

I wonder if anyone has experienced a Florida tax lien being pushed to foreclosure after the 2 years. When the property has a homestead exemption, the minimum bid is 50% of the assessed value (from the previous year it appears). If no one bids, does the tax lien holder have to make up the gap? Also, there are some durable liens such as county maintenance mowing liens that are durable. Is this obligation conveyed to the tax lien holder (foreclosing party) also?