Tolkien owns Glorfindel and the Balrog.
The missing story of the battle between Glorfindel and the Balrog.

Ultimate Sacrifice

Glorfindel, Chief of Gondolin's House of the Golden Flower, stood upon that high place, and the Balrog stood before him, wrapped in fire and darkness. But brave Glorfindel stood his ground, and raised his bow high, his aim true. Thus his arrow flew straight and right, but did little damage to his foe whose skin was tougher then dragon scales.

The Balrog struck against him, its sword smashing the rock above. He ducked away, but was forced to drop, his bow and grab his shield to guard himself. He pulled his sword from its sheath and climbed higher to match his foe. And so they struggled in that high place. The Balrog's sword fell upon his, and mighty was the crashing sound that filled the air from it. The brave elf struggled under the blow and pushed it from him with great strength,

Far below, those that could watch in between battling the enemy at their backs saw a great darkness high in the sky, and in the midst of it, a small light. The dark tried to destroy the light, threatening to crush it, except that the light refused to die.

Thus Glorfindel thrust the sword from his, and a desperate plan entered his mind. He knew he was weakening, and would not stand the Balrog's attacks much longer. But he knew he must save those far below, and so acted out his foolish plan, knowing it would be his death.

He drew back his arm, his sword hung in his hand like a spear, and he shot it from him. The blade looked like a silver bold of power as it sped and true did it hit. The beast let out only one screech of pain as the sword imbedded itself into the place between its eyes, killing it instantly. And so the Balrog fell, crashing into the rock where Glorfindel stood, thus sending them both into the abyss. When Glorfindel struck upon the rocks and his soul fled the flesh. Thus ends the great warrior Glorfindel and his tales until the world changes and he returns reborn. But that is another legend and another time.