Maybe. Or maybe Goodwill got the jacket and the money. We saw a story a few pages back of a Goodwill that got shoes with several thousands dollars in them. Their policy was they hold it for some period of time, but then they keep it.
It seems both unsavory and risky to take $20 from a jacket you know someone else owns on the hope that it's ok because they didn't know it was there.
With the shoes, there were laws that applied- to confirm property above a certain value (depends on state, but usually a few thousand I think) as abandoned rather than misplaced or lost, you have to hold it and publicize the find so that an owner has a chance to reclaim it. So if you find a large bag of cash in the bushes, or somebody's left a new BMW in your driveway for a week with no apparent reason, you have to let the authorities know so that the rightful owners, if there are any, can reclaim it. If they don't, you get a nice visit from the IRS so that you can pay taxes on the value of your windfall.