My wife has late stage dementia, why does she always hold her head up while laying down?

If this is when she is lying on her back, it may be caused by kyphosis. This includes having a posture where her neck is bent forward and having rounded shoulders bent forward. It may not be noticeable when she is out of bed, but then she lies on her back the muscles in front of the neck maybe so tight that she cannot lower their head. This may also be a permanent deformity of the bones of the shoulders and neck. This is common in osteoporosis. The only thing you can do is adapt the bed using pillows to support the head in whatever position already exists. DO NOT TRY to passively move her neck (such as forcing or stretching) as this can cause paralysis or other severe neck injuries. PT here.

No idea, but dementia can cause people to do all sorts of inexplicable things. My cousin, with late stage ALZ, started to keep her eyes closed all the time, even carrying on conversations with loved ones.

Please make sure to make yourself a priority and do lots of self-care. May you receive peace in your heart on this journey.

Just a guess, but her brain may have forgotten that her neck is to relax and lay flat when lying down.
Our brains are amazing and wonderful things and control literally everything we do, and when the circuits start to short out with dementia there's no telling what can happen.