I suspended the back of my car and I have some questions?

That appears to be a parking brake cable. First check if the parking brake works, but on the slim chance it gets stuck on, do that at a place you don't have to walk far if it does. Also be sure to check that it releases freely. A good way to do that is to stop on a slight incline, push in the clutch or shift to "neutral", release the regular and the parking brakes, then observe if the car creeps downhill on its own. If that cable sticks and keeps that parking brake applied, flexing it by hand can often get it released if it isn't rusted solidly tight yet.

You can also follow that cable forward to where the cable comes out of the casing. That will be close to where the front of that casing is attached to a mounting bracket. If the first half inch or so of the exposed cable is shiny, while the rest has the typical dirt on it, that indicates the cable is at least partially applied. If flexing the casing gets that cable to retract under its spring tension, it's a good idea to have it replaced. Sticking cables never get better over time, and no type of lubricant is a permanent fix.

Next, there's a good chance that didn't happen just from this one incident. Look closer at the damaged area and see if the metal that's showing is rusty. That would indicate it's been like this for some time. There's a plastic coating over a metal outer casing, or tube. The concern, if it's still working okay, is water will get in and rust the inner cable to the casing.

Let me know what you find.