This will come down to a discussion with consular affairs locally. Let me talk about two different cases.
In one case, let's say someone wishing to travel to Canada has been intercepted by an airline employee or by a local official because the case doesn't look right to them. They call in the migration integrity officer. The migration integrity officer might do an interview over the phone or might come to the airport and do an interview, and in most cases the case is resolved to the satisfaction of the Canadian wishing to travel.
The other case could be where a Canadian shows up wishing to embark on a flight and discovers that he doesn't have the correct documentation. The documentation may have been lost or stolen. In those cases, again, the MIO will very often be called in, and the MIO will be able to refer that person to our consular colleagues, who may be able to issue an emergency passport or may be able to use their judgment to issue another document that will enable the Canadian to travel back to Canada.