What you have is a Dryer Coin. The Quarter was caught between the drum and the wall of an industrial dryer. Tumbles around until the edge took the appearance it has now.. Not a Mint Error Here is some information - http://www.error-ref.com/dryer-coins/
I won't argue if it's a dryer coin or not. I don't know. It is interesting that the reverse does not show the same effect as the obverse.
It’s too uniform to have been tumbled don’t you think? And most dryer coins I’ve seen have a raised edge.
It could have been lodged in a specific orientation or maybe somebody did something else to mess with it. Regardless, it did not leave the mint like that. It's PMD
Did you weigh it or sandwich in between a few quarters to check for round? That should easily prove to you if it is PMD or not. But happening in the mint in 2014? Laundromat sounds spot on.
Ringers of course. If it came out if the washer it went through the ringer before it went on the clothesline.
I know that is the popular term for these types of details on a coin but in all reality, no one will allow a coin to tumble in a dryer that long. People are funny in the things they do for fun, even if it's just watching a coin roll. When I was a kid, I would ride on the fender of my grandpa's tractor while he pulled a train of loaded cotton trailers to the gin. When we got there we sometimes had to wait in line, just to pull onto the lot. Once while I was waiting, I got to take a tour of the machine shop that served the gin and the oil press. They pressed the cotton seed to harvest the oil, what most vegetable oil is made of. Anyway, all of the shop tools still ran off of a belt and pulley system from the turn of the century. Really cool, even today. But the one thing that I remember the most, was any and every pulley in that shop that had a flat spot on it, there was a coin rolling around in it.
Damaged. Beaten. You are thinking home dryer, think commercial dryer where they run for hours every day, day after day, week after week. Coin gets stuck in those no one is going to bother trying to get it out until the dryer breaks down and needs service.