Can an adult with a drug conviction move to another state and have the case transferred as well?

i know that if your on parole you can sometimes have your parole transferred to another state per the interstate compact agreement. as for this particullar type of case im unsure, but it would seem appropiate that if you were not finished with all court requirements that they could be completed by enrolling in the offender program of the state eg. drug devirsion, or a type of class that would fulfill the requirements of the courts. as for probation that would seem to be accomplished in the same manner as a parole transfer, providing the defendant has a stable home, and family or ties in the state that is accepting the defendant, whereas the defendant would now come under the jurisdiction as a offender of the same state and must then meet those requirements.