Pictures shown below is a typical 32.768kHz crystal, commonly use in Real Time Clock circuit (e.g: DS1307 & DS1337)
Referring to an earlier question posted here, it is a good practice that ground planes should be beneath the crystal. But is it compulsory that we should ground the crystal's body/case too (like what they did in these pictures)? And if yes, what happens if we didn't grounded the case?
One reason may be more mechanical than electrical. Crystals are mechanically vulnerable, and may easily be damaged by shock and (ironically) vibration. Fixing the housing to a larger mass may reduce the effects of those.
Note that, while most likely there will be electrical contact between case and ground in the second picture, I would not rely on it without adding a solder blob at the point of contact. Check it out: hold your DMM's probes on the case to measure resistance. You may have to slightly rub over the surface to see the expected 0 Ω.
I suspect that this may be to short out a parasitic capacitance between the crystal and other parts of the circuit that could affect the frequency of the crystal.
The can is not all that much heavier than the crystal inside. If mechanical energy gets wasted shaking a comparatively responsive can, the resonance quality will be quite worse and the leads and solder points will get more of a strain than desirable. Tieing the can down makes sure that the electrical energy is just spent on making the crystal vibrate: the whole board has enough mass that it can be considered fixed at frequencies of 32768Hz.
