Wiktionary
vb. (context idiomatic English) To become extinct (if a group of plants, animals, or people dies off, all of that group dies over a period of time).
WordNet
v. become extinct; "Dinosaurs died out" [syn: die out]
Usage examples of "die off".
From what seemed infinitely far away there was the cadenced sound of chanting by a chorus of deep male voices, the words blurred and confused by the echoes reverberating from the stone walls and seeming to die off, endlessly repeated.
We shall find ourselves with the same norms of honesty, progress, and humanism, and we shall have made of God an outdated hypothesis which will peacefully die off by itse:f.
If the old horses didn't die off, and you kept breeding at the same rate .
Consider, friend Sulun, that galley slaves on his ships tend to die off at a higher rate than usual.