It's not like there is a large problem in Finland with people living on the streets. Rent is subsidized up to 80% if you are unemployed or without income. Unemployment benefits and/or social assistance cover the remaining 20%. If you become homeless, you will be provided with temporary housing.
Any homeless problems are usually due to larger underlying personal issues. Some people, such as alcoholics and junkies, will not or cannot adhere to basic living rules and will rather choose to be, or forced to be, depending on how you look at it, homeless.
Besides, for a bit of morbid humor, homelessness is a self limiting problem in Finland due to winter.