It's true. Even with the extensive social safety net, programs for mental health, addiction, income assistance, housing provided etc, there is always people who fall through the cracks. A lot of it seems to be addiction (alcohol, drugs) or mental health related, often a combination of the two. Some don't take up the programs, housing, assistance. I don't think the situation can be entirely solved ever, without of course literally forcing people to live in a house or something. That's actually something that used to be done up to fairly late in the 1900s. "Vagrants" could be locked up and made to do forced labour or forced to join the military. I suppose it'd be one way to make the statistics prettier, though even with our current right-wing government, it might be a bit extreme these days.

I don't know the exact way they are enforcing this, but if there are still homeless people then either there are some preconditions to apply or people want to be homeless or government can't afford to house everyone.

In the first case, preconditions shouldn't exist, everyone deserves to not freeze to death. In the second case, there is no real problem, if someone doesn't want to live in a house, than they should be allowed to not live in a house. And in third case, you can't have millioners and billioners and tell the country you just don't have money to house the homeless, tax them and build homes.