I would agree, make copies of the relevent pages showing legal status plus your ID page and passport number.
As for not being safe, if you encountered difficulty in Canada or any country you were visiting, you could obtain consular services and if necessary an emergency document to return to your country of citizenship the same way as if you had lost your passport.
Before sending passports and birth certificates etc it is always recommended that you takes copies.
The only real issue is that you couldn't take a holiday etc or leave Canada except to return "home", but if you're in Canada, who needs to vacation anywhere else immediately, right?

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