I feel I should know this answer but I don't... so I'm exposing my ignorance here. (So far it doesn't hurt too much!)

If someone owns a property free and clear and they don't pay their property taxes one of the taxing bodies will eventually file for a tax sale and the property will go through the sheriff sale process.

My question is: Say the delinquent tax amount including all penalties & fees adds up to $15,000. The property goes to sheriff sale and someone buys the property for $50,000. Obviously $15,000 goes to pay the back taxes and fees, but where does the other $35,000 go? I'm inclined to think that the prior owner wouldn't get it. But if they don't get the excess money, who does?

It is due to the prior owner, however most state laws say the agency only has to notify them at the last known address, which is likely the house that was just sold and they don't live there anymore. So they send the notification, it doesn't reach them, and in a certain number of years the state gets to keep the money. In PA I believe it's 5 years. Some counties in PA are good at finding the owners, others not so much. There are investors and other companies that do this as a business, they find the owners and help them collect the money for a percentage. Look up tax overages investing.

Yes the original owner is due the surplus from the sale. Just like in a mortgage foreclosure, the amount above the mortgage owed is due the owner. However many jurisdictions are not very good at finding the owner and often the surplus goes unclaimed.

This is an old strategy that Gurus are pushing; making a finders fee for claiming the surplus for owners. This is not as easy as it sounds and some states limit finders fees.

an alternative is to sell the currencies to other individuals - coins and cash

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