It is up to the executor to file the tax but you the heir will pay it, either sooner or later.
The executor may ask you for the money if it is in an IRA and you are the beneficiary.
If the executor cannot get the funds from the estate and do his duty, and NJ knows who you are, (they will when you are identified on the Inheritance tax return) eventually the State of NJ will come after you.
Talk to the executor to find out how it is being handled.
