In general I concur in much of what is posted above. In particular, sending a Canadian PR card by courier is OK for probably a large majority of countries. And it is clear many do this without problem.
And, to be clear, so far as I am aware Canada does NOT prohibit doing this.
BUT IT WARRANTS A CAUTION THAT THE DESTINATION COUNTRY CAN MATTER
Some countries have more strict IMPORTATION rules, including as to official documents, and particularly so as to official Travel Documents. Technically the PR card is a status document, NOT a Travel Document (even though many refer to it as a travel document in general usage, given its primary use is to facilitate travel back to Canada), so whether it might run afoul of this or that country's rules, even if it is illegal to import Travel Documents this way, is very country specific.
Reminder: sending anything internationally is subject to the laws of BOTH the country from which it is sent (in this situation, that is Canadian law), and importation laws in the destination country. And, the importation laws for some countries are significantly more narrow and strict than Canadian law. There is a reason why IRCC utilizes the diplomatic process to send documents abroad beyond it merely being more secure and private.
I do not know which specific countries might be problematic. For example, I do not know that Russia, China, or ME countries impose any risk for this but they are among the countries I'd be cautious about and regarding which I suspect are worth doing some relevant homework about before sending a PR card there.
Edit to Add: the extent to which this is done successfully may also be more about a lack of enforcing rules than what the rules are. This is very common in this forum, reports about what is OK based not on what the rule is but on general experience.
For example, there are some strict rules governing sending currency or negotiable instruments (like checks) to the U.S., including when using couriers. I'd guess these rules are not complied with many, many thousands of times every month. Largely because the circumstances or quantities involved are not the real target. And because strict enforcement is very difficult. It appears that the rules are actually overly-broad and NOT applied or enforced UNLESS certain other criteria trigger application and enforcement. I've included cash or a check in birthday cards sent to the U.S. on more than a few occasions over the last two decades, including in courier packets for which the instructions remind one that they are not to be used for cash or negotiable instruments. No problem. None anticipated.
Without researching U.S. importation law, I'd guess that sending a Travel Document by courier to the U.S. is prohibited or subject to special declaration requirements. But again, the PR card is NOT officially a "Travel Document." Moreover, if someone left behind their passport, and had it sent by courier to them in the U.S., it is NOT likely there would be a problem. BUT my guess is that technically that is not OK, at least not without following particular procedures for importing such official documents by courier.
And it warrants remembering that there are more than a few other countries in the world which quite likely have far more strict importation laws and rules than the U.S. And, again, sending anything abroad is subject to the DESTINATION country's laws and rules, totally apart from what Canada's laws and rules are.
