AMS is a spectrum of illness, from mild to life-threatening. At the "severely ill" end of this spectrum is High Altitude Cerebral Edema; this is when the brain swells and ceases to function properly. HACE can progress rapidly, and can be fatal in a matter of a few hours to one or two days. Persons with this illness are often confused, and may not recognize that they are ill.
The hallmark of HACE is a change in mentation, or the ability to think. There may be confusion, changes in behavior, or lethargy. There is also a characteristic loss of coordination that is called ataxia. This is a staggering walk that is similar to the way a person walks when very intoxicated on alcohol. This loss of coordination may be subtle, and must be specifically tested for. Have the sick person do a straight line walk (the "tandem gait test"). Draw a straight line on the ground, and have them walk along the line, placing one foot immediately in front of the other, so that the heel of the forward foot is right in front of the toes behind. Try this yourself. You should be able to do it without difficulty. If they struggle to stay on the line (the high-wire balancing act), can't stay on it, fall down, or can't even stand up without assistance, they fail the test and should be presumed to have HACE.
Immediate descent is the best treatment for HACE. This is of the utmost urgency, and cannot wait until morning (unfortunately, HACE often strikes at night). Delay may be fatal. The moment HACE is recognized is the moment to start organizing flashlights, helpers, porters, whatever is necessary to get this person down. Descent should be to the last elevation at which they woke up feeling well. Bearing in mind that the vast majority of cases of HACE occur in persons who ascend with symptoms of AMS, this is likely to be the elevation at which the person slept two nights previously. If you are uncertain, a 500-1000 meter descent is a good starting point. Other treatments include oxygen, hyperbaric bag, and dexamethasone. These are usually used as temporizing measures until descent can be effected (see physician section for more details).
People with HACE usually survive if they descend soon enough and far enough, and usually recover completely. The staggering gait may persist for days after descent. Once recovery has been complete, and there are no symptoms, cautious re-ascent is acceptable.