They don't end up homeless, they end up packed into houses at densities that Canadian-born people are unwilling to accept. I used to do service/maintenance work as an electrician and you would walk into a 2 bedroom apartment to see 10-15 people from 3 generations living there.
They say we need to increase density but this is actually just decreasing the standard of living. The way economics works, if people are willing to live like sardines to pay the rent, soon people will be required to live like sardines to pay the rent.
I'm not anti-immigration myself and where I live (SK) actually does need more population, but the immigration rate has to be decreased as Canada's public services and housing stock are being pushed to the limits. And something needs to be done about all immigrants ending up in the big 3 cities. Back when Canada was built, they mandated that people move out to the Prairies or other underpopulated areas if they wanted to come at all. That's why we have such a volume of German, Ukrainian, Scandinavian people here in SK - they were sent here and they stayed here, and built our rural communities.