If someone is in a coma can they use a ventilator keep them alive indefinitely?

If a person is brain dead, the heart may continue to function on life support for 36-72 hours max , time to say goodbye. My friend told me his mother was in a coma from cancer and her heart was working when the ventilator was removed. He said it looked like she was suffocating. Is that normal? Can't they wait for the heart to stop before removing the ventilator?