I just went to the States by a car. I had an expired I94 too. Although I didn’t bring it with me. So when I was paying the fee, I asked the officer there what I should do with that. He said I should return it when I leave North America. So as long as I live (stay) in Canada, I can keep it. Or throw it out. They will give you a new one when entering US. That’s what I was told. I thought it was pretty loose, but that was the answer.. But when you leave to Japan, the person at the counter at the airport automatically take it. So don’t worry about it.
By the way, at the US border, they took my fingerprints and photos!! Wehw!!