Florida drivers may elect not to purchase bodily injury (BI) liability coverage. However, many seriously injured by careless drivers are still surprised to find out the other party either had no liability coverage, or carried an amount that could never fairly compensate the injured party. Sadly, nothing can be done about that after the fact.
The simple fact is that you cannot count on other drivers to carry adequate liability coverage. Instead, you should purchase a reasonable amount of UM/UIM (uninsured/underinsured motorist) coverage to protect yourself and your family. This coverage "stands in the shoes" of the driver that carelessly injured you and pays you for your losses up to the limits you purchased.
If you don't know what coverage you have, or if your agent told you that you have "full coverage," it's time to see your agent and ask about UM coverage.