I couldn't make the photo out. but if its only a circuit breaker and there is only 2 wires to each block and this "block" isn't plugging into other wires. or another block.
If that's the case,.. and you need to verify that/this yourself...
If this is so its basically a thermal switch.
The common is common or the "switched leg" or depending... sometimes common is hot (depends on who you ask)that we as electricians refer to in a circuit, be it normally open or normally closed, too much to try and explain our lingo. but the common is common to the open or closed, I've seen it both ways.
Just like a black wire is not always a hot or a ground.. it can be either.
Not to be ugly, but thats why we have meters and know what we do and how to do it.
It sounds like something got HOT if they crumbled.
Try and put it back with new and try not to mix the wires up. they are in that order for a reason.
Mark your wires if need be, take pics of marked wires before it completely falls apart. or draw a diagram of marked wires.
You may pull spade lugs loose from wires then you have to do crimping or hire some work done.
Do 1 set at a time don't tear everything apart and have 50 wires sticking out like a bad hair day and try and figure it out weeks later or the next day after a hangover,. yes people do that. and that gets very expensive like burned up stuff.
"Stuff"= is burned up wires, motors, modules, ECM's computers, cars, houses or boats to name Just a few.
Once you release the "magic smoke" its hard to get that back in.