When (rarely) a tenant is responsible
Rarely. Providing and maintaining hot water is the landlord's responsibility, so a no-hot-water problem is usually theirs to fix. A tenant might be responsible only if they clearly damaged the water heater or plumbing through misuse.
Normal failures — an old water heater, a worn part, sediment, or a plumbing issue — are the landlord's to repair, not the tenant's fault. The narrow exception is when a tenant caused the damage on purpose or through obvious carelessness, which is uncommon with a water heater.
Landlords sometimes try to blame a tenant to avoid the cost of a repair, so be cautious about accepting fault or agreeing to a bill before the real cause is known. If your landlord is pinning a water-heater or hot-water failure on you without a clear reason, a free review can help you understand what is fair.
This is general information about California tenant rights, not legal advice. Every situation is different.