What would you choose? Let a love live but useless or let her have eternal rest?

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During my mother's confinement in the hospital since the accident, right there and then, the doctors told us that it was a hopeless case, no chance for operation, that given the chance she will be alive she will still be a useless vegetable. But still we allowed her to be put in the Intensive Care Unit hoping for miracles. Days past, the situation worsened. She never woke up. So the doctors were there again, telling us it's hopeless, she will still die. They told us that we can sign the DNR (Do not resucitate agreement) if ever she will be having an arrest or we can remove the ventilator which supported her breathing that if taken out, she will die in less than 30 minutes. It took us 2 weeks plus to decide on because some of us couldn't accept it. Good thing another doctor said, that we can have the option to take out or to stop the medication instead of removing the vent, and they made us understand the situation and offered a very satisfying explanation that she will still be useless if alive and if operated on there was 0% that she will be back to normal. So we decided to sign the DNR and the removal of the expensive medications. After two days she died. If you were in our situation, would you do the same? or would you let her live?