What should be done with the surplus amount ($85) over the value of the travel tickets that was given to him, considering that he paid for accommodation ($790) from his own money, and he does not know the value of the fine he will have to pay upon leaving the country due to irregular residency?

The money in excess of the travel ticket price is the right of the questioner, unless the hospital gave him this money on condition that it be spent on the ticket and the remainder returned. In that case, the remainder must be returned to the hospital, whether the employer obligated him to cover accommodation expenses or a departure fine. If they do not have the right to obligate you to these expenses, then you may demand them from them. The basic principle in these matters is to observe the terms of the contract, and if the contract does not specify this, then one should refer to the applicable laws or prevailing custom.