Then one day the Barbarian is fighting a hoard of evil monsters so valiantly and nobly the sword slips free. Barbarian is sad because Tavern Brawler no longer works.
BG3 Tavern Brawler is so busted and is a complete Larian balance-shattering homebrew. Normally you shouldn't WANT to always be using an improvised or thrown weapon the way you do in BG3. That being said, we still have a couple options:
1. The sword can't slip free! It's held in place by magic and the blade itself would sooner snap in half than be freed from its stone by non-magical means.
2. I now have a sword AND an improvised big stone block of slaying with which to throw and bash people about!
In a table top game I would absolutely allow it and find a way to reward the Barbarian for thinking of it
In the spirit of this kind of campaign running, for #2 I'd do something like saying the stone and the blade are still magically linked and drawn together so that the stone block returns to the blade when thrown! Or simply make it a magic stone that deals additional Force or Radiant damage or something.