What I tried to describe is that when exiting JRiver it happens that the audio device JRiver had used would not output any sound after closing JRiver, until a disable/enable cycle is performed. Then you mentioned stop. I tried that too, and it made no difference (I'd found it quite odd if it had made a difference- closing the application has to hand back control of all devices to the OS, no matter whether I hit stop or not).
I now have been cycling through the start JRiver, play something, stop and/or close it, and check other applications. What I noticed is that in some cases sound is restored after a while. I saw it when testing the Windows system volume slider. Moved it to 50%, no jingle sound, but suddenly it jumped back to 100% and sound was there. I could see that several times now. This may be a Windows issue with process closure. I'll keep an eye on it.