Came across this today when doing some state registration docs... New York allows you to search directly for any 'lost money' it applies to things like rebates or refunds from Cable/Utilities companies for when people move home, State tax refunds, bank fee refunds etc... found several entries for my extended family here.
https://ouf.osc.state.ny.us/ouf/
Likely to have a similar search on other states sites..
https://ouf.osc.state.ny.us/ouf/
Likely to have a similar search on other states sites..