Can dwellers die before using all their Stimpaks while exploring?
From the Exploring wikia page:
Outfits increase their statistics and ability to survive, weapons improve their chance to defeat enemies, while Stimpaks and RadAway ensure that they can heal damage and remove any radiation they absorb.
Also, from this answer,
There is no way to force them to use them, they will just use them on their own until their stock you give them when you send them out goes away.
From these posts as well as personal experience, vault dwellers will not die before using all of the Stimpaks you send them to explore with.