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I'd say Group Home in this case. There are various terms used in the US. In general, such places are called "institutions" or homes for neglected children. For teenagers, it's usually a Group Home or a Residential Facility (see below)

Copilarie >> Informations rom eng rus. informations ... social orphans - children abandoned or placed in institutions by their parents ... system for juvenile justice. Teenagers are imprisoned in penitentiary institutions for adults as ...
www.copilarie.md/info_en.htm

HOMELESSNESS ... living in emergency or transitional shelters; are abandoned in hospitals; or are awaiting foster care ... Once placed in a foster home or a home for neglected children or youth ...www.state.ia.us/educate/ecese/is/homeless/doc/lprg04.html

http://www.albanyherald.com/frontsarchive/0303/front030203.h...
Of those children, 7,681 —only a little more than half —were placed in foster care in one of the 3,474 approved foster homes throughout Georgia. Another 467 children were placed in a relative's care, which also is monitored by DFACS. About 1,200 children were placed in GROUP HOMES and 580 in child-care INSTITUTIONS. The remaining were considered to be in an assortment of situations and locations, such as with parents or relatives, or they were runaways.

http://www.free-times.com/Editor/My Turn Archives/myturn0407... ... case of the Carolina Children's Home, its residents are teenagers who've been abused, neglected or abandoned as kids ... he or she is then placed in a residential facility based on ...www.free-times.com/Editor/My Turn Archives/myturn040704.html

One of our purposes is to care for children and provide a safe place for them to live, learn, and grow. In a world desperately needing to turn it's focus on the importance of family values, social service agencies have adopted the policy of keeping families together to work out their problems. Unfortunately, there are times this approach simply will not work. Children, through no fault of their own, are born to parents who are abusive, neglectful, and for many reasons, are incapable of giving their children the care they need and deserve. Innocent children should not have to worry about where their next meal is coming from, having a safe place to sleep at night, or enough clothes to wear.
http://www.noahs-ark.org/the_children.htm

https://en.wikipedia.org/wiki/Group_home