If a store has a "caution - wet" sign posted and you slip and break your wrist, are they still liable?

The store is liable for your injury unless the store can successfully assert the defense of  assumption of the risk.  Assumption of the risk means you recognized and understood the danger and voluntarily chose to encounter it.  For example, you saw the warning sign, but engaged in horseplay on the wet floor and slipped and fell and broke your wrist.

If assumption of the risk is not applicable, then the store is liable for your injury.  You should contact the store's insurance company and verify they are accepting liability before incurring huge medical bills.  Assuming that liability is not an issue, when you complete your medical treatment and are released by the doctor or are declared by the doctor to be permanent and stationary which means you have reached a point where no further improvement is anticipated, obtain your medical bills, medical reports, and documentation of any wage loss.  Your personal injury claim filed with the store's insurance carrier will consist of these items.  Compensation for the medical bills is straight reimbursement.  Compensation for wage loss is straight reimbursement.  The medical reports will document the nature and extent of your injury and will be used to determine compensation for pain and suffering which is an amount in addition to the medical bills.  If you are dissatisfied with settlement offers from the insurance company, reject the settlement offers and file a lawsuit against the store for negligence.  If the case is settled with the store's insurance carrier, NO lawsuit is filed.  If the case is NOT settled with the store's insurance carrier, you will need to file your lawsuit for negligence against the store prior to the expiration of the applicable statute of limitations or you will lose your rights forever in the matter.