Druids that shapechange should not die after shapechanging. If they take damage that reduces hp to 0, they revert to normal form and take any remaining damage to their actual hp.
Druids are altering their physique not crawling inside a separate creature and taking over control. If a druid dies in combat, whether he was a bear at the time or not is immaterial.
That's not how the 5e rules lay it out.
Originally Posted by 5e Player's Handbook
When you transform, you assume the beast's Hit Points and Hit Dice. When you revert to your normal form, you return to the number of Hit Points you had before you transformed. However, if you revert as a result of Dropping to 0 Hit Points, any excess damage carries over to your normal form. For example, if you take 10 damage in animal form and have only 1 hit point left, you revert and take 9 damage. As long as the excess damage doesn't reduce your normal form to 0 Hit Points, you aren't knocked Unconscious.
You take any excess damage to your person, but if you're just reduced to 0 HP when shapeshifted, you simply return to your normal self.