Damage to property you manage would most likely be covered by the owner's property insurance policy. However, the insurance company, as part of the claim settlement, would assume the owner's legal rights (becomes subrogated to their rights) to collect from any person who was responsible for the damage. Insurance companies routinely subrogate to recover insurance payments.
A person may waive the right to recover as part of a contract. This must be done before any loss occurs.
We recommend including a “Waiver of Right of Recovery” clause in all property management contracts. By doing so, the property owner waives the right to legal action against you for property damage that occurs during your management of their property. If your client does not have this right, then their insurance company cannot have it either. Consult with your attorney.