There are many reasons you might have unclaimed funds (abandoned accounts, uncashed checks, misspelled names, incorrect addresses, misplaced inheritance and trusts, etc), and your state is required to hold your property until you claim it.
They will not seek you out, and most people are completely unaware they may have lost funds or property being held by the state.
Every state has an official (.gov) website where you can check whether you have unclaimed property and submit a claim. Just search ‘[my state] unclaimed property’.
e: make sure you go to the official state website; I just noticed some state search top results aren’t the official (.gov) website.
e2: also, check every state you’ve lived in. Moving state is one of the major reasons this happens, and your unclaimed funds will not move to a new state with you.
e3: if you find unclaimed funds, please comment! I’m fascinated to know, no matter how large or small.
Checked this in my state a few years ago, ended up getting like 50 bucks back. Took a while, I forgot about it by the time the check got here. Seemed like the state treasure was happy to have his signature prominently slapped on there.