San Francisco's Patrol Special Police has coexisted with the city's police department for more than 160 years. Now that unique arrangement is on the line as the city's police commission weighs whether to abolish the unusual organization.

Founded in 1847, the Patrol Special Police is a paid 50-person group that contracts out security services to businesses and residents. Under the city charter, its members can carry weapons, wear police-like uniforms and patrol neighborhoods. Funded by the city and through its security contracts,...