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.
When Gotham was isolated due to multiple disasters, Tiegel took on a guardianship role for the Gotham zoo.
Tiegel's grandfather fought on the side of the Nazis in World War 2.
She was once involved in a fight against supernatural forces alongside Catwoman and the very ancient, untrustworthy entity known as Etrigan.
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.