Keep in mind that I don't practice in Florida so there will likely be specific nuances to Florida law here. Generally speaking, you gave what is called permissive use to the licensed driver of your vehicle. Some states recognize a distinction in the scope of permission granted (did you lend them the car just to go to the store and not to do anything else) and some don't. However, and again generally speaking, if you granted permission to the licensed driver and they then gave permission to the unlicensed driver, there is a good chance you (or your insurer) will be on the hook for the damages caused by this unlicensed driver.
Of note, many insurance policies place the issue of whether there was permissive use on what the subjective belief of the driver was at the time of the accident. If the driver subjectively believed that he or she had permission to use the vehicle, then you (or your insurer) could be on the hook. However, keep in mind that some state courts have gone as far as to opine that an unlicensed driver can essentially not have a reasonable belief as to permission. Also important in the analysis is what has happened in the past - did this individual drive your vehicle before? Did the licensed driver lend your car to others in the past? Etc., Etc.
You may wish to consult further with an attorney licensed in your state. However, hoping that you are insured, I would also suggest that you may wish to turn the claim into your insurer. They review the facts and compare the same against your policy and would ultimately come to some conclusion as to whether there was permissive use and therefore whether the claim would be covered by your insurance policy.
Mr. Reichwald's answer was insightful. However, it's not up to you to have to decide whether you'll have to defend a claim arising out of this crash. If a claim is filed against you, then your insurer must defend and indemnify. That's what you've been paying them for. Consult your insurer now so that they are ready if/when the claim is filed.
Contact your insurance carrier to provide you a defense.
Florida adheres to the "dangerous instrumentality doctrine," which may apply under the brief circumstances you provide. Under this doctrine, the owner is generally liable for negligent use of a vehicle, even in cases when the permissive driver allows another person to operate the vehicle.
Bottom line: you need to consult your insurance carrier immediately.
DISCLAIMER: We do not have an attorney-client relationship. Only those persons who have a signed written fee agreement and authority to represent with me is an actual client. This response does not form an attorney-client relationship, nor is it intended to be anything other than my educated opinion or viewpoint. It should not be relied upon as legal advice. I recommend you consult a lawyer if you want professional assurance that this information, and your interpretation of it, is appropriate to your particular situation. Do not act on any information in this response without seeking legal advice from an attorney in your area.
I agree with the other entries in that you should call your insurance company immediately.
Florida law does make a vehicle owner liable for the damages caused when the owner gives permission to another driver to operate the vehicle. This also applies to "second permittees" as in your case where you loaned your vehicle to one person who then loaned your vehicle to another. However, there are exceptions and Florida law does provide some limitation in the amount of damages the owner is liable for depending on the circumstances. Regardless, you need to notify your insurance company of the accident and potential claim. Your auto insurance company should provide some financial protection (depending on the policy you purchased) and a legal defense if required.