There is no single correct way to withdraw treatment at the end of life, and this holds for ventilator withdrawal.

Both terminal extubation (removal of the endotracheal tube) and terminal weaning (gradual reduction of inspired oxygen concentration and/or mandatory ventilator rate) have been used.

The chosen method of withdrawal should be influenced by the same balance of benefits and burdens and respect for patient’s (or surrogate’s) preferences that apply to all medical decision- making.
The patient (if capable) and their family members should be similarly involved in the decision as to how to proceed. The patient should be assessed for responsiveness with verbal and tactile stimuli. The patient should be given anticipatory titrated doses of opioids and benzodiazepines to alleviate any signs of dyspnea after withdrawal of mechanical ventilation.

In all settings after withdrawal of mechanical ventilation, health care providers should continue to titrate opioids and benzodiazepines to maintain satisfactory control of any signs of discomfort. Antibiotics and other life-prolonging treatments, particularly intravenous fluids that can cause respiratory congestion and gurgling, are usually discontinued before ventilator withdrawal.
Although some clinicians prefer terminal extubation, and others terminal weaning, the latter helps avoid noisy breathing due to airway secretions that may disturb the family. If the patient has a tracheotomy, withdrawal is similar to that of the patient who has the ventilator withdrawn while still intubated. A health care team member should be available to the patient and the family until death occurs.
Approximately one-quarter of imminently dying patients have noisy breathing, termed "the death rattle." Efforts to suppress or eliminate the death rattle, therefore, may be appropriate to relieve family distress. Families should be informed in advance of agonal breathing so they can view it is as a part of the dying process rather than a sign of patient discomfort.

Lanken N, Terry B. An Official American Thoracic Society Clinical Policy Statement: Palliative care for patients with respiratory diseases and critical illnesses. Am J Respir Crit Care Med 2008; 177: 912–927.