Hello,
Sorry to hear you are having issues. I am don't have Multiplicity on my system, but have you look at this guide: https://forums.stardock.com/486104/multiplicity-support-faq#mousestuck. 

Thanks
Basj,
Stardock Community Assistant.

Hello,
I have forwarded your problem/question to Stardock Support Team for their assistance. Please keep an eye on this thread for any updates. We appreciate your feedback and patience.

Basj,
Stardock Community Assistant

Probably same issue but a little different because issue started while using the computers, not when shutting down:

The mouse and keyboard split, with mouse on secondary computer, keyboard on primary.

Hotkeys to switch computers did nothing.

Holding shift to move the mouse back to the primary did not work.

I shut down the secondary - no mouse.

With secondary shutdown, hotkeys did not respond.

I tried restarting the service with this:

sc stop multiplicity
sc start multiplicity

Not fixed.

I booted the secondary - the mouse was STILL ON THE SECONDARY.

This should never happen.

Whats worse is I could not use the keyboard to try fixing it, because Multiplicity is not setup for keyboard navigation:  Pressing tab does not visibly move the tab index, and the tab index does not seem to include all the settings.   I'm very disappointed Multiplicity is not designed to handle keyboard-only input, considering the nature of the program!