The executor of an estate has many important tasks. The job requires that assets be accounted for, debts be paid and that assets be distributed under the guidance of the probate court.
Filing tax returns with the IRS is another important task for which the executor is responsible. That can be a problem, if the executor gets it wrong. The IRS will seek to collect any unpaid amount, including penalties and fees, but it may not go after the estate alone.
The IRS might seek to collect the money from the executor personally, since executors can be held personally liable. When that happens, both the estate and the executor have a big mess on their hands.
An estate planning attorney can advise you on creating an estate plan that fits your unique circumstances, as well as advise you on your choice of an executor.
Reference: MarketWatch (June 13, 2018) "When you write your will, don't mess this up."