"Doctor is there anything we can do to save him?"

"Im sorry but your gameboy has contracted Madcatz"

"But what doe that Meeeeeeeeeeeeeeeeeeean?"

"Its a horrible third party desies that inflicts systems with over price and faulty add-ons that break down in a few weeks. Im sorry I dont have better news."

That's simply a Power Handle / Wing Grip (it goes by various names). It expands on both sides to allow the GBC to fit easier in your hands, and includes rechargeable batteries so you don't have to replace those constantly. The thing was commonly sold in combination with an adaptor + car adaptor.

I used have one for my old GBC, made you feel like the shit back in the days.