The act of ditching your current pet at your parent's house because you are tired of it and want to get a new one. Pet drop-offs are most commonly executed by kids who have parents that are pushovers.
Duder 1: "Yo mang, what happened to your suicidal beagle?"
Duder 2: "Oh you know playa, I had to leave him at my parent's right quick. I wanted to get these two cats anyway."
Duder 1: "Whoa dude that's harsh. You said goodbye after all those years by doing a pet drop-off? Damn!"