Unlike most other states, Florida is a no fault state when it comes to car accidents. Everybody that owns a vehicle is required to maintain personal injury protection (PIP) which covers them when they are driving their own vehicle, borrowing one, or a passenger in someone else's car. This covers some of their expenses if they are injured in a car accident regardless of who is at fault.
The goal that the state of Florida had in passing this law was to cut down on the number of liability lawsuits in the state when it comes to auto accidents. Each person's own insurance policy covers their injuries regardless of who is at fault in the vast majority of small accidents. This keeps the accident out of the legal system.
For the most part, one driver can't hold another one liable in a car accident. The exception is if there was a "serious injury" involved which is a term open to legal interpretation. Someone can only file a personal injury claim or file a claim against your insurance policy if they pass the "serious injury" threshold.
If you do carry bodily injury liability on your policy, which generally isn't required by the state, your policy will cover serious and permanent injuries of the other policy up to your limit. If a successful lawsuit exceeds this limit you would be financially responsible for everything beyond that.
To pass this threshold the injured person needs to have suffered a permanent injury. This can include permanent and significant disfigurement or loss of a bodily function. So yes, someone can file a claim against your insurance or sue but it's a pretty high bar to cross and needs to involve a very serious injury.