The minor characters, Jessie's brother Dawson and his wife, her ex-husband Cecil and even her son, Ricky, serve as simply more problematic relationships that Jessie feels unable to understand, help, or manage.
None of these characters add positive reinforcement. For Jessie, human ties are tenuous at best. She is afraid to form them after major disappointments: her beloved father and dog died. The remaining people in her life are held at arms' length, their problems and lives too complicated or dull to inspire Jessie to carry on. They cannot keep Jessie from wanting to die. In fact, just the opposite.