What giant was immortal only as long as he fought in his homeland, killed by Heracles? The giant was Alcyoneus.
Alcyoneus was one of the Giants who opposed the Olympian gods in the Gigantomachy. In Apollodorus’s account, he was immortal while he remained in his native land. Heracles shot him, but the giant revived when he fell back onto his homeland.
Athena then advised Heracles to drag Alcyoneus away from that land. Once outside it, the giant lost his protection and died. This unusual condition is the key detail that distinguishes Alcyoneus from other giant opponents in Greek mythology.
The myth varies between ancient authors. Pindar presents Heracles’s encounter with Alcyoneus as a separate battle and describes Alcyoneus as a huge, formidable warrior rather than clearly identifying him with the Gigantomachy. Antaeus is a common mix-up because he also gained strength from contact with his homeland, but Heracles defeated Antaeus by lifting him off the earth.