Golden Sun simply dumps you back to the nearest Sanctuary, I think. Then again, that series is so easy--with the exception of a few bosses--that dying isn't likely anyways. :V
FF1 Dawn of Souls has something kind of like this, if you die in one of the bonus dungeons you get kicked back to the entrance with like 1 HP, I think. I'm not sure, it's been a long time since I played it.