If you really wanted to go on welfare to get revenge on your wife, you would have to do the following:
Quit your job.
Move to Canada.
Spend all your savings and use up all your time on EI (Employment Insurance) if you qualify for EI.
Once you are penniless and unemployed, go to the welfare office and ask for assistance. You might get something like 500 to 700 a month. In most places, you can probably rent a room for that amount but if you want to eat too, you'd have to go to the soup kitchen or food bank. Because you were sponsored by your wife, she would be requested to pay back the assistance you are getting.
Voila, you have now successfully taken revenge against your wife but in the process, you have made your life hard and you have made yourself unemployed and poor and probably hurt your career as well because a gap does not look good on anybody's CV. You see how this is not the best idea.