You are looking at the box where a phone line connects to the wall. I have unscrewed the plate so the wallpaper can go behind it. There was paint stuck to the plate, and when I pulled the plate away from the wall, some paint pulled away, too.
This shows poor bonding of the paint to the previous surface. You can tell that the yellow paint is latex, because it is stretchy and plastic-y. The green paint below that is probably latex, too. I don’t see a sheen on the green paint, but a gloss finish is one reason that a new layer of paint (or wallpaper) won’t stick. If the previous surface has a sheen, you must first de-gloss by chemical or by sanding (and then wipe off all dust), or use a primer specially formulated to stick to glossy surfaces, such as Zinsser 123.
There can be other reasons for paint not to bond well to the lower surface. Latex generally does not like to stick to old oil based paint. There could be crumbling or flaking, creating an unstable surface.
Either way, it’s important to get the subsurface stable and solid, so paint and wallpaper have something to grab on to, and to prevent peeling or crackling or flaking down the road.