In the most benign cases, it's simply wanting to install home printers that are locally connected on a work laptop when they bring theirs home for the weekend. The answer to this is always no.
Of course, there's also the ones that want to know if they can access the EMR on an outside network (sure that's fine) without connecting to VPN (we'd prefer you do that but this should still be ok) in public (... I don't like the sound of this), when the network is unsecured (ok this is a f***ing terrible idea) and in India (I will beat the living shit out of you myself if you do this)