I recently moved and the cabinets had an awful 3 layers of black paint, no primer. On certain areas when I strip it the grain seems to literally peel off making it look like plywood like pic related. How can I fix this and continue stripping?
Theres some types that are iron on, a little bit like melamine, much like what you'd find on kitchen counter tops, or they are paper thin sheets of wood, normally some sort of exotic hardwood, or any hardwood for that.
They apply a verneer as it can ber alot more decorative than cheaper hardwood ply.
You can apply your own yes, I'm not sure how well it will work though, depending on skill level.
Most are done in a workshop under vacuum pressure. https://youtu.be/UMok_-H1ljs
I've also got no idea why I keep typing 'verneer'. Veneer.
Buy a cabinet skin for the sides, cut to size and glue. Good luck on redoing the veneer on the face, and I hope you can find a stain to match the doors.
They need to be painted again. You're not going to get a good "wood" look out of those cabinets, it would be much easier to paint them a solid color.