Originally Posted by upstater
It sounds like a sticking caliper (or two). While not on my Focus, I have had what seemed similar happen to the L/F caliper on my truck. Horrible burning smell, smoke and heat you could feel from 2' away.
Had that happen on my Neon a couple years ago on the front. I found on neons.org that sometimes the flexible rubber part of the brake line collapses. If you find that the cylinder resists being pushed back in, that could be the problem. Replace the hose, you're good to go.