Is that what happened to dead languages like Ancient Greek and Latin?
No. These languages are considered dead because they are no longer spoken in the form in which we find them in ancient writings. But they weren’t abruptly replaced by other languages; instead, Ancient Greek slowly evolved into modern Greek, and Latin slowly evolved into modern Italian, Spanish, French, Romanian, and other languages. In the same way, the Old English of Chaucer’s day is no longer spoken, but it has evolved into Modern English.