I figured what the box is. It is a junction box. I do not see any exposed wires. I am just nervous that something will short out and the steel wool will be there. Thanks in advance for any help!

That steel wool can be a short term solution but better is to get some caulk to fill that space. You are right to be concerned about that steel wool, often when much younger we would start fires by connecting a battery to a pad of steel wool. The high resistance of that product and the high volume of air inside work to make a very hat and fast fire.

Thanks so much for your help! I am definitely going to consider the caulking method. Another concern is that some of the steel wool has dropped into the wall since we tried to stuff it. Do you think that would become hazardous!? I am just such a worry wart when it comes to fires.

If steel wool is not in contact with electricity it will not catch fire, just eventually rust away depending on how much moisture is present.
I ran across an old Popular Science magazine that had an article about using steel wool and a battery to start your charcoal grill.

Well all of the holes had some sort of wiring running from them. We ended up going a little old school and covering one of the larger holes in the wall with duct tape to see if the little guy enters. I will have to be brave and check it this afternoon. The holes are just so large - whoever did the cabinet work did not think too well. We are going to see if they are still entering that way. The problem is the holes are just too big to caulk up - they need small pieces of sheet rock to finish the holes that were made.