It turns out that the β-amyloids that are cleared during sleep according to this paper, are associated with certain types of dementia in the general population [2].
It also turns out that certain sleep disorders are dementia predictor [3].
This is just a laymen's speculation, but this is suggestive that dementia may be a type of sleep disorder, that it could be caused by some interruption in the process demonstrated in this paper.
And this is a stretch, but it is known that FFI is caused by a malformed prion protein, which is a protein that is deeply involved in various neuron-related functions. It seems possible that this protein is involved in the cleansing process in some way. If so, that would be a HUGE deal, because abnormal prion proteins are associated with a huge variety of neurodegenerative diseases.
Basically, I have high hopes for future research.
[1] http://en.wikipedia.org/wiki/Fatal_familial_insomnia