It depends on the circumstances. If the landlord knew the refrigerator was on its last legs, breaking down, having problems, etc., then there is a good chance the landlord might have to pay for the food, since in that circumstance, the landlord did not act in a reasonable fashion. (Knowing there was a problem, and having a duty to provide the appliances, it is unreasonable to not replace a defective one.)On the other hand, if there was no particular warning, the landlord was not at fault--it did nothing wrong. Without fault, there is no liability and no duty to pay; the landlord is not the tenant's insurer, but is only liable when the landlord does something wrong.