Interesting question there Chuck...Here is TC's answer from the website about what happens when the ADB expires:
(10) When my Aviation Document Booklet expires, do all my privileges for the permit(s), licence(s) or medical certificate(s) also expire?
Yes - You will have to ensure that you apply for a new Aviation Document Booklet before the expiry date. The expiry date is found on page 1 of your current booklet.
Transport Canada recommends that new applications be submitted 90days prior to the expiry date.
Keep the current Booklet until you have received and reviewed the new Booklet. Due to licensing processes, the new Booklet may not show up-to-date licensing or medical certificate information.
If any residual validity period exists, keep the current Booklet along with the new Booklet to provide proof of meeting your licensing and medical requirements.
I take that to mean that if you flew with the ADP expired, you're flying without a license. I would then imagine any insurance company would use that as an out to pay should you have an accident.
Why we can't just go to cards like our cousins to the south is beyond me, instead of this Grade 2, sticker based system. I feel like asking for a gold star every time I go to sim.