Yes, I would give it back and have although it hasn't happened in a while...could be because I hardly ever have cash on me anymore and just use my bank debit card for everything.
I was a bartender/waitress for years and if we gave the wrong change back or dropped money on the floor, it was our loss...it came out of your tips at the end of the night. I saw many many people in tears at the end of their shift when they counted their money and realized they had paid the restaurant to work that night.