US is one of the few countries I’ve been to that doesn’t check any papers at all on your way out (not to say they can’t start doing that).
Edit: I see wikipedia mentions the move to electronic record keeping instead of adding it to your passport: https://en.wikipedia.org/wiki/Form_I-94#Automation_at_sea_an...
It only works for foreigners, I believe, as U.S. residents don't need I-94 forms (the old cardboard slips). I'm also not sure if it works for Canadians, as Canadians can also travel to the U.S. more easily.
Countries that lack strong bilateral cooperation with their only land neighbour have to use other methods, like exit controls.