Although many are close with the families into which they are born, others are marginalized or stigmatized in ways that create deep, lasting alienation between them and their birth families. What do many people alienated from their birth families seek to create

A chosen family

Explanation:

A chosen family is a type of family that is characteristized by the closer relationships among its members. Often times, not necessarily related in terms of biological or legally background, but chosen, specifically for the purpose of shared or connected emotions, love and acting of important roles in one another's life.

A person or individual who is alienated due to marginalization and stigmatization often seeks to create "a chosen family" where he or she gets to feel loved and bond together with other chosen member of the family, like biological family is expected to be.