In the case of brain death, what usually happens is that they will tell the family to gather everyone there who needs to be there to say goodbye, and after x date, life support will be withdrawn. They do not need the family's permission to do this. This probably happens every day somewhere in the US, but we just don't hear about it. Rarely is this challenged in courts, and when it is, the family usually loses and the hospital withdraws support.
If the patient is NOT brain dead: at some point, ICU care will no longer be appropriate and the family will be referred to other facilities that are prepared to offer long term care for a patient in PVS. Insurance isn't going to pay for ICU indefinitely and at some point the ethics committee at the hospital would probably move to have the patient discharged so that the bed could be offered to another patient. The patient might go to a step down unit, or if available, a floor which offers ventilator dependent patients care with a higher nurse to patient ratio than the ICU. It just kind of depends on where the patient is and what kinds of resources are available. There usually is some kind of option available for families who refuse to withdraw support.
