What is the ruling of the Sharia on killing a thief caught in the act of stealing?

This act is reprehensible. The punishment for a thief is cutting off their right hand if their theft is proven by evidence and they stole a quorum from a protected place, not killing, as Allah Almighty said: "As for the thief, male and female, cut off their hands as a recompense for what they earned, a deterrent from Allah. And Allah is Exalted in Might and Wise." The execution of the hudud punishment is the responsibility of those in authority, not individuals. Thus, those who killed this person have transgressed the limits of Allah, slandered those in authority, and killed someone who does not deserve killing according to Islamic law.