Hello,
If (heaven forbid) anything should happen to my father say turning him in to a vegetable. Who would be responsible for him. His oldest child, his ex-wife, his mother, his brothers. By responsible I mean the order to pull the plug and assuming his debit.

If your father would be like that, no one is responsible to assume his debt, any of his property would be attached or sold to pay, and after that they just don't get paid for anything else. At this death if there is anything left in the estate, his estate would be sold and the people paid

He needs to leave a living will as to who would have the right to "pull" the plug. The ex wife has no legal standing what so ever, but in general his childrend could sue for it, but he needs to leave a living will so that it is spelled out who has that authority and what should happen.

You have honest and sincere questions here. This is something to discuss with your parents - their end of life decisions, making a living will, etc. If your Father would become that ill, then it is the family's responsibility to make the decisions. Unless he becomes remarried, then it would be the new wife. The debt or debts fall to the estate and the estate will need to take care of any bills your Father would incur.

Everyone needs to have something written down for those medical decisions - why place the onus on the family?