Sauron was pure evil, except for his ring. However, his ring was still attached to him. The ring really was, like Isildur said, the one beautiful thing about Sauron. However, because it was attached to Sauron's menace, it had to be destroyed. Now, how could it be destroyed? Almost anyone who touched it instantly got attached to its magnificence and couldn't let go. They weren't in love with the ring, though. They loved it personally, for its power and grandeur.
Golem, however, loved the ring's power totally and absolutely. He saw something special in the ring. No matter where Golem turned in his life, there was despair and hunger. When he saw the ring though, he was free from all that. It brought him a glimmer of peace.
Isildur's bane killed him, but Isildur showed compassion for the ring. He knew that to destroy the ring would be to destroy the basic goodness that was within Sauron. That would mean making Sauron totally evil.
Yet Sauron threatened to bring doom to all of humanity if he returned. This was imminent. Sauron was destroyed by Golem loving Sauron with true devotion. The ring was the opposite of Sauron, yet made by Sauron. Golem became one with the ring, and disappeared forever.