How can I help someone with mental illness who is socially withdrawn?

Socially isolated. Many mental heath disorders can damage the social relationships. Be supportive, encourage social contact, minimize stigma and try to educate people about the illness.Depressed anxious people avoid contact because of our society's harsh response to people with mental health problems.No one avoids or looks down on some one with hypertension or asthma, but with depression anxiety a different story.
TREATMENT. Support and affirmation are great but ultimately professional help is necessary. A therapist and possibly medications. Evaluate for depression and anxiety for instance.