There are laws in place to prevent the utility companies from cutting off heat in situations like this.
From: https://www.needhelppayingbills.com/html/utility_and_heating...
> Texas - State law requires that utility and gas companies are required to offer a deferred payment plan to families and individuals in the state. No disconnect can occur if customer agrees and adheres to payment plan for past utility or heating bills. No shut off is allowed if temperature is to go below 32 degrees, or in extreme heat. Also disconnection will be delayed if detrimental to the health of a state resident, but the customer must have physician certification to get this plan.