If it's coming off easy you should not /don't want to get that skimmed, if the current isn't bonded correctly you should take it all off.Plaster itself.
Tbh I noticed it coming off soo easily when I was Stripping the wallpaper
If you have solid wall construction (ie no cavity) you should be aware that modern methods eg dot and dab or gypsum based plaster and hardwall aren't breathable and can cause damp problems. You should read up on lime based plaster products and take a view on this, info on the Internet will be better than I can offer.