Nothing has changed and you can still own uninsured and unplated cars. One of my cars is effectively uninsured and unplated for a few months each year when it goes into the garage for winter storage. I cancel insurance in the fall, and don't bother renewing the sticker or insurance until spring when I'm ready to start driving it again.
Your scenario is something else. Anyone can sue anyone else in Ontario for almost any reason at all.
If your bike is stolen by a thief who then causes injury to a third party, the third party can certainly sue you. Your bike did the damage and you as the bike's owner are responsible for what happens when your bike is used.
Your defence will be that the bike was stolen, but the injured party will come back and say that you failed to take all reasonable steps to keep the bike from being stolen. You will say that you took the key out of it. They will say that this was inadequate and that the bike should have been chained up inside a secured building and the bike further secured with an ignition immobilizer and even by pulling the battery. You will claim that you did your due diligence, and they will try to paint you as negligent.
You may ultimately win in the end, or not, depending on who has the most persuasive argument. With the costs of litigation being what it is, you may simply decide to throw some money on the table to make the third party go away.