There is a 41 year old Muslim sister who was born a deaf-mute & dumb; she recently suffered a heart attack and is currently hospitalized in critical c

Question

There is a 41 year old Muslim sister who was born a deaf-mute & dumb; she recently suffered a heart attack and is currently hospitalized in critical condition. After the heart attack, paramedics administered CPR and/or use of a defibrillator - attempting to resuscitate using electric shock, which has since caused further damage to the sister's brain, and deteriorating condition. The medical staff has induced the sister into a coma, and pronounced her as brain-dead. Doctors and medical staff have implemented a tube over her nose for breathing, and a tube down her throat for feeding. Doctors are now "advising" her kin that the air and food tube must be removed after 12 days to prevent further infection. Today is the twelfth day. The doctors would like to perform 2 different surgeries, one on her stomach, and the other on her throat. A stomach surgery will implement a tube of some kind, or apparatus to allow for feeding of liquid food. A similar surgery will be performed on her throat to allow for a fixed breathing tube, or respirator. Allegedly, both surgeries will leave the sister in a state that would require professional medical assistance for the remainder of her life, while she is in a coma. Such special medical attention is received from special homes, or facilities for people in similar medical situations. The family members are gathered at the scene in the hospital. Some relatives would like the respirator and feeding tube removed, while others would like to proceed with the doctors recommended surgery. Is it permissible to remove the current feeding & oxygen apparatus, and wait for Allah T'alla to issue her fate? Removal of all these devices will essentially starve the sister of food and air according to the doctors, since she can not function or use her body and organs on her own. If the family decides not to do this, the alternative is the proposed procedures by the surgeons, then placement into a special care facility; is such an act permissible? Please advise. Jazakallah Khair.