Yes, but not exactly. On August 25th, 1944, Robin Olds was flying an escort mission over Germany in a P-38 fighter when he noticed a flight of Germany Messerschmit-109's below him. Olds and his wing man jettisoned their external fuel tanks and dove on the German Messerschmits. However, Olds neglected to switch his fuel intake valve from the external tanks to internal ones, so his engines immediately cut out. Still committed to the dive, Olds fired on the German aircraft, destroying one before pulling out of the dive and restarting his engines. To my knowledge this is the only confirmed example of an air-to-air kill where the attacker had no working engine, but I'm open to any examples that prove otherwise.

Olds went on to serve through the Vietnam war, eventually ending up as a Brigadier General. His memoir, Fighter Pilot: The Memoirs of Legendary Ace Robin Olds, describes this encounter in more detail.

On April 29, 1944, the day after his promotion to Hauptmann, Heinz Knoke claimed a P-47 with his engine dead and his right wing on fire. He had shot down a P-47 several seconds earlier before his Bf-109 ran out of fuel, but his target's wingman continued firing at him as he approached the ground. When his engine died he reported that the P-47 behind him overshot him, failing to adjust for his decrease in speed. He fired on the aircraft and crash-landed several meters away from where his American adversary had landed after bailing out. Knoke was credited with 33 confirmed kills during the course of the war and 19 unconfirmed claims, but Knoke's "kill," who spoke with him for several minutes before ground troops came to secure the allied pilot, had his identity confirmed as Captain James Cannon, and was transported to a prisoner of war camp