RESPONSE BASED ON PERSONAL EXPERIENCE
(Please note I posed the question only so I can share my own experience for others' benefit, I am not seeking an answer from others)
I am in Canada on a W-1 visa and work permit.
Just prior to leaving Canada on a work trip, I discovered my work permit was missing. I immediately filed for a replacement document
here, and then left the country taking with me photocopies of my work permit, replacement application, and payment receipt for the replacement application.
When I returned to Canada, the officer at the gate asked to see my work permit and, because I did not have an original, directed me to an immigration officer. I explained the situation to the immigration officer and showed them proof that I had already applied for a replacement document. They checked my work permit online, and admitted me.
My general suggestion if you lose your work permit:
1) When you discover your permit is lost or destroyed, IMMEDIATELY apply for a replacement permit
here. Note that this may require filing a police report, depending on the circumstances.
2) Preferably, you should try not to travel in the 2 weeks or so it takes for a replacement permit to arrive.
3) If you already have pre-booked out-of-country travel and expect to be gone for a long time, then have the work permit sent to your out-of-country address. If you are going for a short trip of less than 2 weeks, then carry with you copies of your replacement permit application.
4) At the port of entry, be forthright and clear about your situation so the immigration officer can help you appropriate.