Flaking Cabinet Edges

I'm looking for a temporary fix to a messy problem.

The base of the 20 year old cabinets in the kitchen are formica on some sort of particle board (the drawers and doors are formica on solid wood). The raw edge under the counter top and near the floor has begun to disintegrate so whenever you wipe under the edge your sponge (and the floor) is covered with wood particles.

We'll be replacing the cabinets next year, but I need a way to seal these edges in the meantime. Any suggestions?

PuppyMom welcome to the forum, I hope you will enjoy it.
The only (cheap, because you will replace it anyway) solution I can think of is to spray some plastifying coating on it after you have stuffed some glue to hold it together.

Not sure how visible the bottoms are, but you can also use a primer/sealer called BIN - made by Zinsser. It's not made to be a "finish" product but it should hold the particles together. Might need two coats to cover fully.