If you don't take care of an abscess what harm can it do?

Worst case-DEATH. Depending on where it is, the microbe that is causing the infection, and the size of the abscess itself, an abscess can eventually lead to a blood infection (e.g. Skin/soft tissue abscess- blood infection- heart infection) or infection of an adjacent structure (epidural abscess- brain abscess), causing overwhelming infection and death, or at least major disfigurement and handicap.