Correctly dealing with crumbling basement walls
Is there a way to repair this...

It's a lath and plaster wall, probably on furring strips. Remove anything that's lose and patch the holes with easy-sand or durabond (chemically setting). If it's bad enough the plaster might need to all come off and then drywall it, unless you can raise someone from the dead who can actually do plaster.

... to prevent future debris from accumulating?

That's the hard part about money pits. Intentionally removing any other lose plaster will give you more time until you'll need to do it again. But that's a band-aid on a foundation issue: water ingress.

But you patching the walls every decade is a lot cheaper than having drain tile installed around the outside perimeter of your house, and if you have a relatively dry basement with no flooding or seepage issues; not really worth it. Just make sure the grade is away from the house, and keep your gutters clean.

The other, somewhat excessive, option is to tear it all off and parge coat the foundation with the appropriate mortar. If the seepage problem is minimal, that should last the rest of your life. Again, you'd need someone who knows how to trowel, or it will look like a parge coat.

A picture might help, but I wouldn't be able to feel how lose all the plaster is. Use your best judgment. If large parts of the wall flex in the slightest, it should probably all come down. But it's a basement, maybe you don't really care; then patch and paint it with whatever (chemically sets). But when parts start falling off while you drag a paint roller over it, you know what you should have done.