Here is my guess.

Spouse #1 dies and there was a Family Living Trust. A Marital Trust was established with Spouse #1's assets in it and it should have an EIN and it should have been filing return. (B of the A/B Trust) All of the income from the Marital Trust is generally distributed to Spouse #2

Spouse #2 dies and the Family Living Trust now gets an EIN (A of the A/B Trust) and will file it's first (and maybe last return)

The current Trustee would be the one to apply for the EIN (or you if they authorize you to do so.)