If you were in fact negligent, or careless, in causing the grease fire, then  you would be liable for any property damage. However, (1) if you disagree, you can make them sue you and prove it (and present any evidence, etc. in your favor)--they must be able to prove your negligence if you go to court; and (2) you are only responsible for the damage actually done by the fire even if you are at fault--the landlord can't use this as an opportunity to remodel. Given how much they are trying to get from you, it's worthwhile consulting wiith an attorney about the situation--it's possible that if there was fraud, you may even have a counter claim of your own.Finally, if you are found liable and have to pay an unsupportable amount, don't forget bankruptcy as an option.