General maritime law survives the Jones Act. I almost never pay attention to personal injury claims. But I once made my living litigating admiralty cases, so McBride v. Estis Well Service (5th Cir 10/02/2013) caught my eye.
Workers on a drilling rig were killed and injured, and that led to a suit under the Jones Act claiming negligence, and also under general maritime law claiming unseaworthiness. Plaintiffs asked for punitive damages, but the trial court dismissed all claims for punitive damages. The 5th Circuit reversed.
Long before the Jones Act came along in 1920, general maritime law allowed claims for maintenance, cure, and unseaworthiness. The Jones Act makes no reference to unseaworthiness, so it is well-established that a seaman retains the right to sue for unseaworthiness.
A closer question is whether punitive damages are allowed in unseaworthiness cases. The 5th Circuit says they are, assuming you can prove "willful and wanton breach of the general maritime law duty to provide a seaworthy vessel."
It's funny though, because the doctrine of unseaworthiness is a no-fault system.