Posters on this forum relate that if you have genuine emergency, you must include cover letter/evidence of urgency, and then they will process your PR renewal application relatively quickly. I don't know how fast, but some say it takes short amount of time. Others travel for emergency purposes and apply for travel document from abroad, to get back to Canada, and include the same evidence/cover letter they would for PR renewal. You may need copies of your tickets, among other things.
I really don't know much about fast processing of urgent cases, but if you post a thread about it you may get responses you seek.