In Bava Kama page 22 R. Yochanan holds the liability of fire is because of his arrows. But to Reish Lakish fire is obligated in damages it belongs to him. Neither say openly whether the obligation of guarding an animal so that it will not go out and cause damage is on the person in whose domain the animal is, or the owner. But a braita in Bava Kama page 45 says there are four types of guards, free, for pay, a renter, and a borrower. If the animal goes and kills someone, they all have to bring the kofer [restitution] and the animal is killed, and the guards pay the cost of the animal to the owner. However, the unpaid guard does not have to pay the owner for the cost of the animal because he did his obligation of guardianship. The gemara there says the case is where each one guarded the animal with minimum confinement. If the there would be an obligation on the unpaid guard to pay damages because the animal was in his domain and guardianship, then he would not be exempt from the cost of the animal. Rather, we see it is the owner who pays damages [like Reish Lakish, and the liability of damages is on the owner, not the person guarding the animal as is clear in the Rambam himself in the beginning of law of damages ] The other guards would pay back the owner, but not the unpaid guard. The reasoning here is if the case was not of killing, but of the animal causing damage, and the unpaid guard had an obligation to people that the animal caused damage to, then he would be required to do maximum confinement like the other guards.---------------------------------In בבא קמא ר' יוחנן holds the liability of fire is because of his arrows. But to ריש לקיש fire is obligated in damages because ממונו. does the obligation of guarding an animal so that it will not go out and cause damage is on the person in whose domain the animal is, or is that obligation on the owner? A ברייתא in בבא קמא דף מ''ה says there are four types of guards, free, for pay, a renter, and a borrower. If the animal goes and kills someone, they all have to bring the כופר [restitution] and the animal is killed, and the guards pay the cost of the animal to the owner. However, the unpaid guard does not have to pay the owner for the cost of the animal because he did his obligation of guardianship. The גמרא there says the case is where each one guarded the animal with minimum confinement שמירה פחותה . If the there would be an obligation on the unpaid guard to pay damages because the animal was in his domain and guardianship, then he would not be exempt from the cost of the animal. Rather, we see it is the owner who pays damages (and thus decided the רמב''ם himself in the beginning of ה' ניזקי ממון.] The other guards would pay back the owner, but not the unpaid guard. The reasoning here is if the case was not of killing, but of the animal causing damage, and the unpaid guard had an obligation to people that the animal caused damage to, then he would be required to do maximum confinement שמירה מעולה like the other guards.