I don't know about Canada laws, but in USA, you can go on welfare while living with someone, but they go by the income of others living in house as well, not just yours.
In the USA, there is no real welfare. They only give you X amount of money(like almost nothing, like around $100) for an X amount of time and they make you work for it. If you can't work, then you have to meet all these requirements that were purposely designed to be extremely difficult to meet so a lot of people who need welfare can be disqualified... You can get food stamps for 3 months for free but that is it. Afterwards, you will have to work for it or meet all these requirements that were purposely designed to be extremely difficult to meet for the same reason above. Because the people in power, don't want to spend any tax dollars on helping people. Social workers don't treat people like shit or ignore them for no good reason... It's all a part of a plan to discourage people from trying to get help from the government and make people lose faith in the government. Welfare in the USA is a myth, created by right wingers to trigger people. If you are disabled, you can get free money for life(called SSI) but they make it so difficult to be officially seen as someone who is disabled so most likely, you wont be seeing any of that money even if you are literally too mentally and/or physically crippled to work the kind of jobs that are available. And even if you are able to be officially recognized as a disabled person according to their insane requirements, a judge could just tell you to fuck off anyway or make up some BS excuse like, "Well you can still work a desk job so fuck off." For the few lucky ones who are able to get SSI, it takes them years and years and that's with the help of a good lawyer. Most of this stuff is really there just to trick Americans into thinking there are safety nets when there really aren't any safety nets... You are pretty much on your own. Battle Royale style unless you are fortunate enough to have loving family and friends. There is a reason a lot of people CTB after losing their job... Because they know, the only thing that awaits them is dying slowly on the streets.