Presumably, the person who suffered damage is alleging Negligence on your part.
Most jurisdictions say that there are four elements to a negligence action:
- duty: the defendant has a duty to others, including the plaintiff, to exercise reasonable care,
- breach: the defendant breaches that duty through an act or culpable omission,
- damages: as a result of that act or omission, the plaintiff suffers an injury, and
- causation: the injury to the plaintiff is a reasonably foreseeable consequence of the defendant's act or omission.
Well, 1-3 are pretty much open-and-shut. Its possible that you could argue 4 - that it was not foreseeable that your cigarette in the trash could cause the damage that it did. However, I think you are fighting an uphill battle - fires, by their nature, can do a lot of damage and that is foreseeable.
You seem to be arguing for comparative negligence which reduces your liability to the extent that the plaintiff contributed to the damage.
You would have to prove that the "fire proof trash can" a) actually exists and b) is a reasonable thing for the plaintiff to have foreseen the need for and to have provided. Its far more likely that a reasonable thing would be to have provided a trash can for trash and an ash tray for cigarettes. Of course, if they did provide an ash tray and you didn't use it then they have no comparative negligence.
You could make a similar argument that the BBQ was not adequately maintained. or that it was not reasonable to allow smoking.
However, this would all be a very, very long shot - you started the fire so prima facie you are liable for the damage.
The person who suffered damage is only entitled to recover their costs - they can't make a profit. It doesn't matter if the bill is "huge" it matters if its reasonable. For example, the bill for the International Space Station ($150 billion) is huge - its also reasonable.