Across Europe, rates of homeless have only increased over the past several years, except in Finland where rates are decreasing. Finland is the only EU country that has initiated a housing-first approach to homelessness, which through organizations such as Y-Foundation, provides housing to people experiencing homelessness without conditions. This means that someone who is navigating substance, mental illness, or in a position where they're unable to pay rent, are allowed to receive housing as part of the program. Residents are expected to pay rent, but social workers help residents apply for State benefits so they can meet their needs. The program thus far has been a major success.
Roughly 20% of residents end up homeless again in the future, which means the success rate is far, far higher than under other models. The number of people experiencing homelessness is now manageable to the point where shelters have enough capacity to meet people where they're at and provide services. The country is also spending less money by providing housing, social services, and benefits than it previously did.
Here are rates in Finland over the past couple decades:

Quote (Finnish Homelessness Strategy (2015))
During the programme (PAAVO I 2008–2011 and PAAVO II 2012–2015), approximately 2,500 new dwellings have been constructed and acquired for the homeless, and approximately 350 new professionals in housing social work have been hired to work on homelessness. Shelters have been replaced by modern housing units, the quality and safety of housing have improved, and the prerequisites for social rehabilitation related to housing have improved. By investing in prevention, and in housing guidance in particular, it has been possible to prevent approximately 200 inhabitants per year from becoming homeless. Most importantly, long-term homelessness has decreased by approximately 1,200 persons from 2008 to 2014, and homelessness continues to decrease.
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Housing sustainment statistics are not collected in a uniform way across Housing First services. However, reports from service providers and policy makers are that rates of housing sustainment are generally very high. Only very low numbers appear to have abandoned or been evicted from apartments in the Housing First services in Helsinki City, during the last year, for example. The longstanding statistical monitoring of the long-term homeless population is seen as a key indicator of the success of Housing First. In 2008, 2,931 people were long-term homeless in Finland, in ten biggest cities, falling to 2,192 in late 2013, a reduction of 25%. Long-term homelessness fell from 45% of all homelessness to 36% of all homelessness in Finland between 2008 and 201121. This is a major achievement in which the use of Housing First services played a crucial role.
Quote (Action Plan to End Homeless 2016-2019)
During the programme to reduce long-term homelessness (PAAVO 2008–2015), the Housing First principle has been implemented in the work on homelessness and shelters have been replaced by housing units based on supported rental housing. During the programme period, long-term homelessness decreased by 1,345 persons (35%). In 2015, homelessness decreased for the first time to fewer than 7,000 people.
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According to studies, housing one long-term homeless person saves approximately €15,000 of public funds per year. The work on housing guidance by the City of Helsinki saved approximately €1.5 million in the costs of the city’s rental housing companies in 2015 while ensuring the continued housing of hundreds of tenants by preventing arrears of rent from becoming court cases.
Sources:
https://www.ara.fi/download/noname/%7B0707CEDD-2854-4EA0-ABDD-352120B49731%7D/145931https://helda.helsinki.fi/bitstream/handle/10138/153258/YMra_3en_2015.p df?sequence=5http://asuntoensin.fi/assets/files/2016/11/ACTIONPLAN_FOR_PREVENTING_HOMELESSNESS_IN_FINLAND_2016_-_2019_EN.pdf