Sub panel without a ground wire
Are you suggesting it does not have a grounding electrode conductor? Or an equipment grounding conductor? Or a grounded conductor?
If it is a panel fed from another panel it generally does not require a grounding electrode conductor (unless in a separate structure).
If it uses metallic conduit or EMT the EMT or conduit can serve as the equipment grounding conductor.
If there are no L-N loads no grounded conductor is actually required.