Filing a will in probate court does not prevent a service provider like a phone company from expecting prompt payment. Although few companies shut down home service the minute a customer misses a payment, it is within a phone company's rights to turn off service if a deceased customer's bills go unpaid.
Utility companies expect payment for services provided regardless of whether the client ordering the services is living or dead. This is not as unreasonable as it seems. Although the deceased won't be using the home telephone, others staying in or visiting the house might do so.
Once the will of the deceased is filed in probate, an executor is appointed to administer the estate. Often the will names the executor, but if not, the court usually appoints a family member. The executor is charged with several duties, including paying estate bills, including telephone bills.