I used to put Hoppe's cleaner/M-Pro 7 on the brushes, CLP from the back of the brushes for the next 6 inches or so and Hornady's One Shot w/Dri-Lube to the loop, loop dry, so it acted like a patch.
Now I use the snakes or Otis ripcords as a quick cleaner after a shooting session, so I spray the first third of the snake with CLP and let it go at that. If I lived in a more humid state I'd probably continue to spray a little One Shot on the back of the snake/ripcord, as it apparently has a bit better rust protection than Breakfree.
I've only had a snake get stuck once, in my .22 Henry AR-7, but fortunately the loop was still hanging out of the breech, so I just put the barrel in my vise and pulled it out. It was really stuck and I had to put most of my body weight behind it to get it out. Of course, it let go quite suddenly and I almost threw myself out the window when it came loose. After that, I haven't used snakes for my .22s. Never had one get stuck in any other caliber bore. I do like the idea of tying a length of para-cord to the loop though.
As for cleaning snakes, once I ran them through the washer; the boss threw a pretty serious fit over that, so now I drop them in a 5 gallon bucket, fill with about two gallons of hot water and mild dish soap, let them soak for an hour, agitate every fifteen minutes, rinse and let air dry.
And I only wash them twice a year. Once in February (beginning of reloading season) and once in August (right before fall fishing season).
One way to get the worst of the crud out of a snake is to blast it with Hornady One Shot. A lot of the black soot, metal shavings, etc. will come out, and the One Shot dries pretty quickly.