In my experience, if/when a mouse or keyboard becomes disconnected from the PS/2 port while a machine is running it will not return to operating status just by plugging in again. A reboot was required. USB is designed for hot swapping. PS/2, Parallel and Serial ports were not and attempting to do so carries a risk of damage to the motherboard.
I guess when I retired from the company that made the ps/2 I missed the point about it being a hot plug. Not it is not a hot plug device. People do it and the fuse was raised and the circuit change to let silly people do it but it was and is not a hot plug device. Only usb and more modern connections are.
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