Property uninhabitable due to tenant negligence

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Property uninhabitable due to tenant negligence. Tenant left heat off while on vacation causing broken pipes and property to be flooded for 1-5 days based on when event was discovered by landlord.  No answer yet if landlord’s property insurance will approve claim. If insurance denies claim, landlord does not have the financial ability to pay for extent of damages. Tenant admits to turning heat off. Property located in upstate NY. Can tenant hold landlord accountable for habitability and timely repairs when they admit to turning heat off? 

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Thank you for the response. Per lease, tenant is required to have renter’s insurance, does not specify including liability. Landlord will need to amend and specify that in the future liability coverage must be a part of renter’s insurance.