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If at night, the corpse is cremated.
If during the day, the rubble is pulverized.
(The notion of pulverizing the undamaged stone corpse of a gargoyle who has died peacefully in his sleep is disturbing. But in fact, gargoyles so rarely die peacefully in their sleep as to make this a non-issue.)
In either case, the cremated or pulverized remains are taken by the gargoyle mourners to the highest point on the local map. A memorial is held. Everyone who wishes to speak of the departed, may. No one, not even the departed's enemies, may be denied a voice. In the end, the mourners spread the remains upon the wind, saying, "Ashes to ashes OR dust to dust. All is one with the wind." (Over time, humans began to use a variation of the same at their funerals.)
The gargoyles then spread their wings, soaring amid the ashes or dust in the hope that part of the departed will stay with them forever.
[Note: There was no one to perform the wind ceremony for Coldstone, Coldfire or Coldsteel. That, and the location's ambient magicks coupled with the trio's own passions, may explain their accessability to Demona's ressurection spell.]
Even in peaceful times, Gargoyles -- even very old gargoyles -- all but never died in their sleep. Sleep for gargoyles is borderline suspended animation. If an old, weary Gargoyle actually made it to daylight and stone, that bit of sleep would tend to freeze the aging process, the deterioration if you will. Rejuvenate the gargoyle even just a little bit. They'd be much more likely to die after the sun went down, after transforming back into flesh. Even before the iron age, when Gargoyles had little to fear from most any species, when turning to stone was an excellent daytime defense and not a liability, most ancient Gargoyles died just before sunrise, after an exhausting night, rather than after the sun had risen.
So again, the disturbing notion of surviving gargoyle mourners having to pulverize a perfectly preserved stone corpse is a veritable non-issue. The practice of reducing stone remains to dust was a result of gargoyles having to come to terms with stone-sleep having become a vulnerability. If you're loved one is already rubble, there isn't much reason to keep the rubble intact. That doesn't mean the process isn't emotionally painful. But not much more painful, I would think, then cremating a corpse of flesh. (Though of course it's more immediate. You are doing the damage, not the Fire.) At any rate, that was the custom that evolved.
GargWiki.net has answers for all your Gargoyles questions.
Features include episode commentaries by series co-creator Greg Weisman, interviews with the cast, and a documentary on the annual convention.