The executors are responsible for the physical payment but have no financial liability. The situation with Estates having no liquid assets is not uncommon and if the executors send a copy of the death certificate and confirm when probate was applied for and that the property is being marketed and asked for some indulgence with regard to the payment of bills, the executors will find that the various creditors will grant some leeway with regard to payment to allow the house to be sold to realise the money to pay the bills.
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If you are staying in the property on your own, would be liable for all the bills and maintenance plus, three quarters of the market rent would achieve if on the open market, and you would be liable to pay that to the other 3 beneficiaries if they asked.
The executors always can ask the creditors to grant some leeway but the creditors may ask for proof that there is a genuine attempt being made to liquidate the assets and your occupation may be seen as a barrier to that.