Happily, this wasn't actually the case. Canaries faint long before they die and miners would carry small resuscitation chambers where the canaries could be reawakened in an oxygen-rich atmosphere. The Science and Industry Museum in Liverpool has one in their collection: https://blog.scienceandindustrymuseum.org.uk/canary-resuscit...
Interesting, but I frankly doubt the birds remained utterly unharmed. Birds are really sensitive to many gases, with the common anecdote being to not cook with nonstick pans if you have a parrot.