I believe this was missed during check-in because their work visa still looks valid.
Airlines only check if you have the necessary documents for the destination for one journey (most of the times, either outbound or inbound). They generally do not check if you have the correct documents for your return trip.
But if their Canadian visa indeed still looks valid to airline staff, it is a good thing.... (read on)
Is there a mechanism by which I could give my partner this missing document (e.g. via airport or immigration staff)?
Not really. You would depend on the good will of the staff.
But this does not matter.
If your partner can appear physically before a Canadian border agent for examination, they do not need a PR card. It is their constitutional right to enter Canada; once they say the words "I am a permanent resident of Canada", the border agent has to make reasonable efforts to ascertain their status and must allow them entry into Canada once their identity and status as a PR is established. If your partner has a non-expired PR card, their file and status can relatively easily be looked up electronically. Of course, in practice, it is always a good idea to put the border officer in a good mood, since the agent has the authority to hold a person until their status can be established, so be polite.
But that's only if they can appear physically at a Canadian port of entry. The problem is, if you are not travelling back to Canada by land from the U.S. using a non-commercial means of transportation (e.g. private or rental car, bicyle or on foot), an airline or another commercial transportaton company will only let you board their plane (or bus, ferry etc.) if you can show them that you have the documents to enter Canada, e.g. a Canadian or U.S. passport, a visa, an ETA, or a PR card or travel document.
If their Canadian visa still appears valid even if technically it has ceased to have effect by virtue of their permanent residency, it is likely that they can still board the flight back to Canada and appears for examination before a Canadian official. But this may still carry a risk of being refused boarding if the visa was cancelled in the database.
Otherwise, without a permanent resident card or travel document, a visa-required national cannot even reach Canada by commercial means.
In some cases where the person concerned has a U.S. visa, it is often suggested that they take a flight to Seattle or somewhere close to the Canadian border and appear for examination before a land border post; or if they are eligible for visa-free transfer at a Canadian airport, they can change their itinerary to "transit" through Canada (but in fact forfeiting the outbound trip from Canada once landed in Canada).
U.S. passport holders or legal permanent residents do not have any problem since they do not require any other document to travel to Canada. Visa-free nationals may need to obtain an ETA (even though they are technically ineligible).