“Wraparound” is widely used in mental health case management programs, usually reserved for people with severe illnesses who may be able to be kept functioning in the community if intensive and flexible services are provided, but who would otherwise require more expensive treatment in inpatient or residential facilities. In that world it carries two main connotations: (a) assembling a multi-agency team serving the same patient or person; and (b) paying for services or needed items that would not be allowed in a fee-for-service insurance program oriented to strict “medical necessity”. (For example, wraparound funds could be used to provide a respite caregiver, to pay overdue utility bills for the family, or to buy school clothes for the child patient.)
The term came into general use in 1984 with the passage of federal legislation establishing CASSP teams and services (Child and Adolescent Service System Program). See history on page 5 of URL