Did your father own a home or have pension/retirement benefits from his place of employment or have other assets? If so, then those need to be handled and transferred to his heirs by having a probate done at the county courthouse. When probate is opened, the assets are assembled and outstanding bills are paid from whatever is in the estate. And the heirs get anything that is left over.
If there will be no estate because there are no assets, then you can simply send a letter (to the company that sent you the bill) to explain that there is no estate and the bill will unfortunately have to remain as unpaid.
Does the bill explain what services were given and the dates they were given? The bill is probably legitimate if they provided services to your father while he was still alive. If you have enough money to pay the bill, then please do so, but if it would cause a financial hardship, then you are NOT personally obligated to use your own money to pay it and they can not come after you to do so.