Is it permissible to claim one is traveling for Hajj in order to receive the value of annual travel tickets in cash, so as to benefit from it instead of borrowing, and does sin fall upon the Hajj campaign that assists in this?

If the department stipulates that an employee must travel to obtain tickets, then it is not permissible to falsely claim to have traveled in order to obtain them. This is based on the Prophet's (peace be upon him) saying: "Muslims are bound by their conditions in what is lawful," and "Beware of lying, for lying leads to immorality, and immorality leads to the Fire." Similarly, it is not permissible for Hajj companies or others to assist in such actions, for Allah Almighty says: "And cooperate in righteousness and piety, but do not cooperate in sin and aggression."