Matt stumbled on Vault 13 and was captured by the intelligent deathclaws living there. They give him freedom of movement within the lower levels of the vault, but he is never allowed on level 1 where the exit is. Matt sees the intelligent deathclaws as a threat to humanity, and wants to escape so he can see them wiped out.
After you have agreed to help Matt escape the Vault, you will be at the first floor. The deathclaws there will start attacking him but not you nor anyone in your party unless you attack them first. If Matt is killed and you haven't attacked any of the Deathclaws you are free to leave the screen. But when you come back to the Vault there might be a bug which will shut down your game. [verified]