Just out of curiosity - how do you survive 3 years without working? Lol.
The person needs to have some kind of income like a gift from relatives, or disability support, or EI or whatever it maybe and that will force you to file taxes.
The only weird scenario I can think of is if you are a high roller gambler or if you hit the lottery. Those windfall incomes are 100% tax exempt in Canada but you are still obligated to file taxes I would say. Lol.
Either ways, unemployment does not stop a person from becoming a citizen.