What happens to Fleance in the play Macbeth?

Fleance is, of course, the son of Macbeth's friend and comrade Banquo. Macbeth comes to regard Banquo as a threat because he also saw the witches' prophecy and because the witches foretold that Banquo's descendants would be kings. Macbeth assigns assassins to murder Banquo and Fleance while they are out riding. The assassins are successful in killing Banquo, but Fleance escapes. We do know Fleance's sons will emerge to rule Scotland. Indeed, some at the time (including the King himself) traced the lineage of James I, king of England, to Banquo. Fleance's escape thus had modern relevance to Shakespeare's audiences. We are not told where Fleance went after escaping the murderers, only that he survived the attack.