What is the prognosis for a brain stem stroke, 7 days ago, still on ventilator?

It depends. The prognosis depends on many variables, such as the patient's age, other health conditions, and underlying cause of the stroke. However the need for mechanical ventilation a week out is, in general, not a good sign.
Indefinite. In general coma from a brainstem lesion lasting one week bodes poorly. If diaphragmatic weakness, without coma is present, the prognosis is only slightly better.