Property maintenance responsibility

Unless there is an agreement specifying who pays what, both parties have the obligation to pay the whole.  Only a court can adjudicate a division.  Holding joint title to an income producing property without an agreement is a guaranteed problem.

Your co-owner certainly does have a responsibility for half of the upkeep of the property, regardless of whether he resides there. You have many options. Assuming his share is not his only asset in his irrevocable trust, his trustees may be able to pay his bills- so send the trustees a bill for his share of expenses.  If renting out a portion of the property is possible, that is another option; while you'd normally have to share any rental income, if there's no contribution to expenses you'd be entitled to an amount equal to the co-owner's share of unpaid expenses.  Your best option is to buy him out, if possible, as this will end the entanglement. As a last resort, you could sell the property and split the proceeds and as a very, very last resort, if the trustees refused to sell, buy you out or be bought out, you'd be entitled to a judicial partition of the property if you went to court.