Found money is money in a person's possession that the person has forgotten about and rediscovers at a future date. Although this term is also sometimes used in reference to money that someone finds and takes possession of, like coins found in the street, in the financial world, it is specifically used to describe money that a person already owns or controls. A bank account someone opens and forgets about and later finds records for is an example of found money; the person had the money all along, but was not aware of it.
While it might seem odd to forget about a bank account, money stashed in a pocket, or other sources of money, found money is actually very common. Many banks have very large lists of inactive or dormant accounts owned by people who have forgotten they have them. Likewise, many government agencies have accounts due, like tax refunds, to taxpayers who have moved or become impossible to locate. That money belongs to those taxpayers but can't be passed on to them because the agency can't find them.
People find out about found money in a number of ways. Sometimes, people rediscover funds when they are going through old financial records, or turning out a pair of pants for the washer. In other instances, a financial institution or agency manages to track someone down in regards to a dormant account so the funds can be restored. It is also possible to look up listings of dormant accounts or outstanding payments due to see if there are any funds in a person's name floating around. By convention, dormant and unclaimed assets go to the government after a set period of time, and the government is obliged to maintain records about these assets and make them available to members of the public searching for assets in their name.
Usually, a government agency handles unclaimed property, and people can contact the agency with their names and identifying information to see if the agency has any records pertaining to unclaimed property in their names. After providing proof of identity, the assets can be transferred. Simply restoring assets to a person who already controlled them does not incur any tax expenses, but people may owe taxes on earned interest, in the case of interest-bearing accounts that have been neglected for extended periods of time. People can get information about the tax implications of found money from an accountant.