A convicted felon is not advised to travel to Mexico. The Mexican authorities will send the person back to wherever he or she came from if they were to find out.
Although a person may have a valid United States or other passport, Mexico authorities do not allow convicted felons to enter their country. Whether it is by plane, ship or any other means, a convicted felon who tries to enter Mexico will not be allowed to disembark from the ship or leave the airport if the Mexican authorities get word about his felony conviction.
The person will be sent back to wherever he came from immediately. In worst-case scenarios, the person may have to put up at the airport for days to go back.