MULT and VGR (VTAM Generic Resources or GRS) are not related.
VGR exists to support the ability to run multiple copies of TPX under the control of the same VGR name and have VTAM and WLM handle the distribution of the individual sessions. VGR does not exist to support MULT users.
MULT works the same in or out of a VGR environment.
When a MULT user is signed off or disconnected, all the sessions for that instance of the MULT user are ended. That is why a MULT user cannot "get back to" an active session. There is none to get back to.
If the session, such as CICS, is not properly cleaning up the session that TPX inactivates then the cleanup process for that application, CICS, should be investigated.