The sums are a pittance — spare quarters and dimes, perhaps less in some cases — left behind on the unwanted MetroCards tossed to the station floor.

But add a few together, the thinking goes, and a downtrodden rider might have enough for a swipe. Combine a few more, and perhaps a job seeker who is homeless can find his way to a few interviews.

And if there was a means to recover all of the more than $50 million in unused balances wasted annually by New York City’s transit riders? Then, Zachary DuBow thought, he would really be onto something.

So Mr. DuBow, 24, a consultant and recent New York University graduate, founded the Next Stop Project, in February. He would collect discarded MetroCards, ask station agents to aggregate the remaining balances into full-fare cards, and distribute them to needy residents — ideally partnering with the Metropolitan Transportation Authority to gather the forgotten passes.