shederr wrote:
The problem is that on the corner of the
wall (which is rounded), the paint has peeled off in large chunks
exposing what looks to be plastic underneath. Is it plastic?

if it looks like plastic, it's plastic. If it's an outside corner
there have been multiple options to make these solid, most common is
metal, but I have seen paper and plastic used for these applications.

the entire wall be constructed of this? What can I use to patch this
up?

If it doesn't feel like drywall then it's whatever you thought it was
in the first place. Patch where the paint is flaking with paint....

And, for my future reference, is there an easy way to maybe even
cap off the wall with a nice looking wooden cap or something?

maybe, you'll have to look around.

Thanks!

No problem. If you'd like further assistance please take a picture
and post it or be much more descriptive.