Is it permissible for a worker to take the difference in wages from his employer without his knowledge, believing it to be his right, because his wage is lower than the market rate, given that he is an undocumented resident?

If you agree with a man upon a certain wage, it is not permissible for you to take more than that without his knowledge and consent, because it is consuming people's wealth unlawfully. Allah Almighty says: "And do not consume your properties among yourselves through falsehood." You must repent to Allah and return what you took to him, even if indirectly.