This 1981-S Cent Escaped.

They are out there, I don't know why, but they are.

Cool!! Maybe some acetone? I'd give it a soak.

Correct. Acetone (100%) will soften/lift certain soiling but wont affect the patina of the coin. Acetone essentially neutralizes oils that transfer from handling, so its more conservation than cleaning. But experiment on expendable coins to learn a bit about the soaking process. Verdicare helps slow environmental factors and removes the verdigris but it will not restore a damaged coin. Your proof would probably be best cared for with Verdicare rather than acetone. But acetone will lift some light soiling/crud that will loosen and float off.

Experiment first with conservation on expendable coins. Acetone is available at Walmart amongst other stores for about $1 for a 6 oz bottle.

Well if ever there was a coin to experiment with cleaning that might be one . I found some circulated proofs before and I find usually all they need is warm water and a dish soap diluted and just let it sit for a couple seconds then pat dry. I have also found you can put some pressure on them depending on the towel you use to dry. I have a few microfiber towels that I used to use detailing cars they all have old car wax built into them even after they are washed. As long as nothing is stuck to the towel I have never left a mark. Now my disclaimer. I for one would never do this to a nice proof . Also I take no responsibility in any damage you might cause to a coin. Seriously though if you do want to try start light and little and then slowly see what you can get away with. At least then you will know amd you won't ruin anything worth a lot of money

Well I got myself some 100% acetone and gave it a whirl on some quarters I got today. One had green 'paint' all over it, and it all just came right off and turned the acetone green, leaving an entirely different looking quarter - nice and shiny. That was cool. It also helped remove some crud off other coins, but didn't do anything for stains, which I gather that you can't do much for stains. So, are soak times based on the concept of whatever works and doing the least amount of soaking that will get the job done? Also, is there a duration that would lead to damage? Thank you!

These 60 bicentennial halves all had S on them?

Nevermind, I think I figured out why it says S. I think there were Susan B Anthony S coins in the unc sets of these two years. It just appears as if there are S coins in every denomination of unc sets at first glance. I thought maybe my cent was from one of these sets after seeing they had S that year, and given the look of my coin, but alas, this cent can only be from a proof set.

I didn't even think of that as being a reason for how these end up loose, thanks for pointing it out.