They don't unless thr country has a tax treaty with canada. However if you stop filing tax returns in canada they will be a bit annoyed/suspicious. I would think you would want them to know you are no longer living in canada to avoid paying the tax?
I suspect that if they take an interest in you it would be pretty easy to check with customs to see when and how often you were leaving canada.
Canada has a pretty good expat friendly tax system...better to play within the rules imho than try and cheat it and get busted for thousands in back taxes and penalty's.