I want to know, is there any law under which one person could transfer his case from one state to another state?
 

I think as per the category of post I presume that it is a criminal case.  So the accused can file petition before the supreme court of india to transfer the case from one state to another state.  For details clarify your local lawyer

Transfer will be allowed only if there is sufficient material to show that the prosecution will act in a biased manner in that particular state.

Person was working as Cashier in Co-operative Society, (Modi Rubber Upbhokta Sahakari Samiti Ltd.) during his hopitalisation period, he was suspended by the company with allegation of fraud by giving him letter at home. Company also file case against him u/s 420 etc. in 1997 in meerut (UP). In 2008, person has won the case in court. Person had filed appeal in 2008 for his pending salary, but till he did not receive any update from court for releasing his salary.

Person is now living with his elder son in delhi, as he does not have any sources of income meerut. In that case whether he is transfer his case in delhi from meerut. It is not possible for him to go date from delhi to meerut.