Is it permissible to feign illness in order to obtain resignation from work?

Merely pretending to be something does not count as a lie, because it does not involve conveying information, and lying is intentionally conveying information contrary to reality. If there is a fixed-term contract between the young man and the factory owner, it is not permissible to use deception to get out of it, because Allah Almighty says: "O you who have believed, fulfill [all] contracts," and because the Prophet, peace and blessings be upon him, said: "Muslims are bound by their stipulations." However, if the contract is not fixed-term, then either party may terminate it whenever they wish, and the young man may use legitimate stratagems, such as pretending to be something he is not, to get out of the contract.