Depends on the jurisdiction. In the US, each state has escheatment[0] laws governing how untouched accounts are retired and how they may be subsequently claimed by their original owner. That process typically happens through a government agency rather than through the original company that held the account. But other parts of the world have other processes.
That doesn't seem logically related (though that doesn't mean it legally isn't). If there's a statement from last year saying that the account has x amount of money in it, then that's a document within the 10 year retention even if the last deposit was more than 10 years ago, so there's still a record that the account exists.
