In most cases, if a trust has bills that it has to pay or debts that have to be paid off, those things will be paid out of the trust estate by the trustee. One of the trustee’s jobs is to pay for all the expenses and debts of the trust estate.
Trust Beneficiaries Do No Pay Expenses of the Trust
The trust beneficiary may have their share of the trust reduced when those expenses and debts are paid out of the trust estate, but a beneficiary is not responsible for paying the trust expenses or trust debts out of their own pocket.
Beneficiaries should never be expected to pay for the expenses of the trust or to pay creditors of the person who created the trust who’s now deceased. Those are all expenses the trust pays and the trustee should be paying those before you get your distribution. It may reduce what you get out of the trust, but it should never reduce what you own separate from the trust.