What is the ruling on one who went out to steal during Hajj? Does he receive the reward for Hajj and get punished for the theft?

Stealing is a major sin, and its حرمة (sacred inviolability/prohibition) increases in the sacred months and during the Hajj season, especially when committed under the guise of worship. The target of such theft, in this context, refers to the guests of the Most Merciful (pilgrims).

Anyone who commits such an act will have nothing from his Hajj except punishment and a bad reckoning due to the corruption of his intention.

If the intention was solely to steal, and he wore the garments of Ihram (definition) merely to cover up his crime without intending Hajj, then he will have no share in Hajj except sin and punishment, for the Prophet, peace and blessings be upon him, said: "Indeed, actions are by intentions, and indeed, every person will have what he intended."

If he set out with the intention of Hajj but also intended to steal, his Hajj is valid, but he has committed a grave sin. This is because Allah Almighty has ordained severe torment for merely intending atheism and sin in the Sacred Land, as Allah Almighty says: "And whoever intends therein to deviate with injustice – We will make him taste of a painful punishment." (22:25) And His saying, the Most High: "So whoever has made Hajj obligatory upon himself therein [by entering Ihram], there shall be for him no sexual relations and no disobedience and no disputing during Hajj." (2:197) This falls under the type of acts about which scholars say: "He disobeyed and it was valid."

If he combined both intentions (Hajj and theft), the ruling depends on the dominant intention.