A Irrevocable Living Trust agreement is manditory, but the trust appears to cease unpon the death of the beneficiary.

"This trust shall cease and terminate
at the death of the beneficiary, or earlier if the trustee determines that the existence of the
trust is no longer necessary to establish or maintain Medicaid eligibility for the beneficiary."

Would the grantors SSN be appropriate even though an Irrevocable Living Trust agreement is manditory?

No. Irrevocable trusts are not grantor trusts. Only grantor trusts can use a grantor's SSN. The trust must have its own number.