Debbie Tiegel began a career as a detective in the Gotham City P.D. and was later fired when she uncovered corruption in the ranks.
Debbie and Tommy ran into each other on several occasions where they ended up aiding one another.
At first disgusted by Monaghan, the wise-cracking hitman grew on her. She and Monaghan had an on and off relationship because she despises what Tommy does for a living but obviously still cared for him.
It obviously ended when Tommy died.