What is the church's responsibility when discipline is begun and the "offender" leaves their church? Is there no more responsibility to continue?

As far as I can tell, the NT does not specifically address this scenario, but logic woul suggest that the church should still be told of the offenders refusal to be disciplined and then to contact any church that the offender tried to attend to update them on the situation. Sometimes as person will refuse discipline in the church where the offense occurred, but accept discipline and help in another church for obvious reasons. The main thing is to work toward the recovery of the person in some way. In the mean time, Paul' admonition in 2 Thess to continue to warn the offender, avoid intimate association, but continue treat them as a brother is pertinent. See 2 Thess 3:14-15.