I bought a new bath fan for my old house(1920s). Where the fan is installed, there is a power/black, and a neutral, but no ground wire to connect to it. It's old knob and tube wiring. Is no ground pretty common with old houses? The new fan has a black, white, and a green wire, is there a safe way to install it? What should I connect the green wire from the fan housing to? What is the danger of leaving it disconnected?
The danger of connecting the green wire to a ground that doesn't go all the way back to the panel is that if the fan has a ground fault, the ground wire will not carry the fault back to the safety of the panel, and instead will distribute the ground fault to everywhere on that island of grounds. So all the grounds will suddenly become hot.
I would leave it disconnected.
I would also assure that this section of the circuit is protected by GFCI.
I would also see that the entire circuit is protected by an AFCI breaker back at the panel.
These have totally different jobs; the AFCI protects from arcing overheat loads caused by failing wires. The GFCI protects humans from shock due to lack of grounding.