Unusually Severe Desquamation
Desquamation (from the Latin desquamare - to scrape scales off a fish) is simply the peeling or shedding of the outermost layer of the skin. It happens to everyone when skin cells are replaced every 14 days or so, but the cells are generally unnoticeable, as they don't shed in large sheets.
When skin is damaged or burned, like in a sunburn, desquamation becomes more noticeable and occurs in sheets and flakes. Some of the diseases that commonly afflicted kids, like measles and scarlet fever, caused significant damage to the epidermis, causing (sometimes very significant) desquamation after the rash dissipated.
This child had scarlet fever with a markedly more severe rash than most, but with other symptoms within the average range.
Diseases of Infancy and Childhood. Louis Fischer, 1917.