Like in the US, "homelessness" as in "poor or unlucky people who find themselves without a residence" is practically a nonexistent problem. The real problem is the mentally ill or drug addicted people frankly being a public nuisance.
Finland has tried to sell their strategy as one of providing housing, but that masks the actual reality. Finland is engaging in large-scale involuntary confinement of mentally ill individuals, and that is responsible for the entirety of their solution.
The current Finnish mental health regime was enabled by a law passed in 1990. Since that point, given the 5.6M population times the 214/100,000 rate [3], we get a total of ~12,000 people committed. The graph in the linked article [4] shows a reduction in homelessness from about 17,000 to about 4,000, a reduction of approximately 13,000 people.
So all but a tiny fraction of the homeless population was not miraculously housed; they were put involuntarily into mental hospitals. While I hope that Finnish mental health facilities are humane and the inmates are well cared for, historically this has almost never been the case -- other agencies claim credit for reducing homelessness and eventually funding dries up and the conditions worsen in the facilities because the problem doesn't seem urgent.
[1] https://news.ycombinator.com/item?id=42656711
[2] https://news.ycombinator.com/item?id=42683898
[3] https://www.cambridge.org/core/journals/psychiatric-bulletin...
[4] https://oecdecoscope.blog/2021/12/13/finlands-zero-homeless-...