Is it permissible to kill or maim a person who has entered the house with the intention of stealing, knowing that handing him over to the authorities will not result in the law being applied to him?

If theft is proven against a person by evidence or confession, then the authorities must carry out the punishment of cutting off the hand, based on the Almighty's saying: ﴿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, Wise.﴾ It is not permissible for individual Muslims to kill or harm the thief, in order to avoid chaos and a breakdown of security. Even if the authorities are unable to apply the law, that is less severe than the chaos that would result from individuals applying the punishments. You are permitted to kill or harm the thief to prevent them from stealing if they resist and you find no other means, but you will need to prove their aggression before the authorities.