If the accident scene was not visited by the police and the accident is minor, the driver can decide to not declare the accident. However, that means that he/she will sustain any repair costs or medical bills.
When it comes to auto insurance, Florida is a no-fault state. In "no-fault states", drivers have to carry auto insurance that pays personal injury protection benefits. They can also carry property damage liability and additional, optional coverage as the one for bodily injury liability. Thanks to these regulations it may be easier to secure money after a single-vehicle accident even if the driver was at-fault.