Do I need to file a tax return for my deceased father?

I have gotten conflicting answers and advice from people on this subject. Let me start by saying that I am the executor of my Dad’s estate, which was not very large. Therefore, any tax implication will be minor. In other words, he would not be getting much in the way of a refund nor would he owe much. Since I have not done the paperwork, I am not sure how it will come out, but it will be close to breaking even.

My real question is: What are the implications to his estate (and me, as the executor) of not filing a federal return? If taxes are owed and not paid, I assume he could be audited just like anyone else. Would the IRS be willing and able to track down his heirs? If so, what would the statute of limitations be on that?

I already know that the law says a tax return must be filed, so I am not wondering about the legality of not filing. I am just trying to determine the possible implications of not filing. Thanks in advance!