Most bulbs are high switched, so when not powered there's a path through the bulb down to chassis - the main exception is the interior light, which is normally low side switched, so will have 12V on both sides of it when not lit.
Usually, it will show 0V or very near that, relative to chassis ground, in a vehicle using filament lamps.
It's not a *direct* connection to chassis, as the circuit is via the lamp.
It will usually be quite low resistance if it's a working (not blown) filament bulb, but may not show any connection with a normal multimeter in the case of LED lamps.
There are now a lot a lamp assemblies in cars that have some sort of electronics in them. Some have power connected to them all the time, and some signal that is not the power goes to them to tell them to turn on.
One example is LIN controlled multicolour ambient lights.
(On one of my cars, the lamps are at +ve when turned off, but it is quite old and is positive earth, so probably not what we are talking about here.)
I can think of a few reasons to ground a signal that is turned off.
It could be to prevent an LED light from glowing of flickering due to a monitoring circuit or other leakage. It could also be to prevent the monitoring circuit from flagging a fault when the LED is turned off.
If a normal DC motor is being supplied, shorting it when off will slow it faster. On reversing motors, the side that's not being connected to 12 V has to be connected to ground to complete the circuit, so two circuits like you have shown may be used.
There is very rarely harm in shorting out a load that's not in use.