Debbie initially appeared as a background character within range of Strickland and occassionally seen in his company during some of his more controversial acts, such as abandoning his business in times of trouble. It was not subtle that the two were in an extramartial affair, much to the chagrin of Strickland's wife Elizabeth "Mz. Liz".
Fed up with her husband's actions and seeing him at a propane gala with Debbie, Mz. Liz takes control of Strickland Propane, dismissing Buck from his position and making Debbie a tank-wipe. To protect his business from being in her possession, Buck signs over his restaurant Sugarfoot's to Hank although it is transitioned to Peggy. Over time, the Stricklands start to reconcile their differences and Hank is briefly made the manager of Strickland Propane.
In the meantime, Debbie is spurned by Buck's reconciliation with his wife. Enraged, Debbie tries to come onto Hank, stating that she intends to have an affair with her boss. Being a loyal husband, Hank rejects Debbie which enrages her as "nobody rejects Debbie Grund". Debbie later tries to get back at Hank by exposing a nonexistent affair to Peggy, only for the call to be intercepted by Hank while Peggy is operating Sugarfoot's. Debbie then blackmails Hank into meeting up for sex lest she frame him for having an affair.
Debbie takes a scattergun with Mz. Liz's name engraved upon it and hides in the dumpster behind Sugarfoot's. She intends to kill the two but is mysteriously killed via unknown means. Hank is framed for her murder although it is soon revealed that Debbie had attempted to juggle the gun, nachos, and a large drink while climbing into the dumpster. With bad timing, she accidently shot and killed herself.
Prior to her death, Debbie showed some signs of being a dumb blonde stereotype. For example, when told by Buck to act as discretely as his eyes and ears, Debbie openly repeated that to Mz. Liz.