Taking a patient off a respirator and the ruling on mercy killing

Firstly: 

It is not permissible to remove or withhold the respirator
from a patient except in the case where it has been definitely established
that he comes under the ruling of one who is dead, because all brain
function has completely ceased, or his heart and breathing have completely
stopped in such a way that the doctors have determined is irreversible. 

It says in a statement of the Islamic Fiqh Council belonging
to the Muslim World League, issued during its 10th session on 24/2/1408 AH:

In the case of a patient whose body has been hooked up to
life support, it is permissible to remove it if all his brain functions have
ceased completely, and a committee of three specialist, experienced doctors
have determined that this cessation of function is irreversible, even if the
heart and breathing are still working mechanically with the help of the
machine. But he cannot be ruled dead according to sharee’ah until his
breathing and heart stop completely, after the machine is removed. End
quote. 

It says in a statement of the Islamic Fiqh Council belonging
to the Organisation of the Islamic Conference, that was held during its
third conference in ‘Ammaan, the capital of Jordan, 8-13 Safar 1407 AH/11-16
October 1986 CE, after the presentation of all points of view on the topic
of life support machines and listening to detailed explanations from
specialist doctors: From a shar’i point of view, a person is considered to
have died, and all the rulings that apply to death come into effect at that
point, when one of the following signs appear:

1.When his heart and breathing
stop completely and the doctors rule that this cannot be reversed

2.When all his brain functions
cease completely and specialist, experienced doctors determine that this is
irreversible and necrosis has begun to occur in the brain.

In this case it is justified to remove life support from the
patient, even if some of these organs, such as the heart, are still working
mechanically due to the action of the equipment. End quote. 

Secondly: 

So-called mercy killing is not permissible, whether it is
done by withholding treatment from the patient or by any other means. It
comes under the heading of haraam killing which the Prophet (blessings and
peace of Allah be upon him) regarded as one of the major sins. There are no
exceptions to that except what has been mentioned above concerning one who
comes under the rulings of those who have died. 

As for withholding treatment on which life depends on the
basis of reducing the suffering of the patient and putting an end to his
pain and suffering, it is not permissible and this comes under the heading
of haraam killing. 

Al-Bahooti (may Allah have mercy on him) said in Kashshaaf
al-Qinaa’ (5/495): It is not permissible to kill it — meaning the
animal — or to slaughter it for the sake of giving it relief, because it is
wealth so long as it is alive, and slaughtering it is destroying it, and it
is forbidden to destroy wealth, like the human who is suffering from painful
disease, because his life is protected by sharee’ah so long as he is still
alive. End quote. 

We ask Allah to heal your mother and grant her well-being. 

And Allah knows best.