I have not had time to check all my books but there is some hints about Beorn in FotR
Fellowship of the Ring: Many Meetings
Quote:
Frodo learned that Grimbeorn the Old, son of Beorn, was now the lord of many sturdy men, and to their land between the Mountains and Mirkwood neither orc nor wolf dared to go.
'Indeed,' said Glóin, `if it were not for the Beornings, the passage from Dale to Rivendell would long ago have become impossible. They are valiant men and keep open the High Pass and the Ford of Carrock. But their tolls are high,' he added with a shake of his head; `and like Beorn of old they are not over fond of dwarves. Still, they are trusty, and that is much in these days.
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So far it is not certain if he has died or simply left the area but he did have a son who ruled meny men.
I will see if I can find more info.