Skinning animals alive is a rare event, whit most animals skinned it represents an undesirable risk for the individual doing the skinning.
Some animals used for meat and fur produce higher quality meat if they are bled to death and a stunning blow is delivered to enable the animal to be bled out it our struggle that would hurt the handler or the meat, this bleeding step can be combined with the skinning but that practice has faller out of favor because it bloodies the pelt.
Strictly speaking animals never need to be skinned; In the developed world a variety of alternative to animal furs exist (though this answer does not answer the question)
Individuals with strong stomachs can search for "Chinese fur trade video" in any search engine and find a video of a Chinese fur farm skinning live animals, purportedly the reason is that it is faster and or easier to skin them alive, it is unclear that this is true.
Human animal abuse for the sake of animal abuse is common enough to explain the majority of these cases.
