typically, an equipment failure does not confer liability either direction unless it was caused or ignored by one party. unless you did something to it or ignored manufacturer's instructions for maintenance, if any. I don't see how this is your fault or the tenant's fault


I would advise tenant to file a claim with their renter's insurance if it covers this kind of loss. Personally I would offer to cover 10/19ths of the june bill, as the bill would have been that much less if you had investigated immediately when your tenant complained on june 9th but I don't believe you are legally required to.