Why did God promise to spare Ebed-melech's life when Jerusalem fell?

Answer: He had trusted in the LORD

God told Ebed-melech, "I will surely rescue you so that you do not fall by the sword... because you have trusted in Me."

“And while Jeremiah had been confined in the courtyard of the guard, the word of the LORD had come to him:”— Jeremiah 39:15 (BSB)