A dog that jumps down or a goat that climbs down and breaks utensils is an unusual Hezek and pays Chatzi Nezek.
Rebbi Yochanan holds that Esh is Chayav as if it was your arrow and Reish Lakish holds that it is only Mamon ha'Mazik. (1)
If a dog grabs a hot biscuit with a coal and takes it to a stack of grain and eats the biscuit and sets the grain on fire it pays Nezek Shalem on the biscuit and Chatzi Nezek on the grain.
According to Reish Lakish the dog threw the coal on the grain and it pays Chatzi Nezek on the place where the coal landed and it is Patur for the rest of the stack. (2)
According to Rebbi Yochanan the dog placed the coal on the grain and it pays Nezek Shalem for the place where he put it down and Chatzi Nezek for the rest of the stack of grain. (3)
If a camel loaded with flax went into a store and set the flax on fire from a fire that was in the store and burned the store down it is Chayav to pay. (4)
If the storekeeper placed a fire outside his store and the flax caught on fire the storekeeper is Chayav for the flax, however Rebbi Yehudah says that if it was a Ner Chanukah he is Patur for the flax.
If someone sets a stack of grain on fire and there was a goat tied to it and a servant next to it he is Chayav for the grain and the goat.
If the servant was tied to the stack of grain and the goat was next to it he is Patur because he is Chayav Misah for the death of the servant. (5)
If a person is Chayav Misah for killing someone and at the same time he causes a monetary loss to someone else he is Patur from paying.
Someone who sends a hot coal with a deaf-mute, insane person or Katan is Patur from Dinei Adam, however if he sent a flame with one of these people he is Chayav according to Reish Lakish because it is a definite Mazik.
Rebbi Yochanan holds that even if he sent a flame with one of these people he is Patur because it was the act of the deaf-mute that caused the fire.
Rebbi Yochanan holds that if he sent dry wood, twigs and a candle together with a deaf-mute he is Chayav.
A BIT MORE
1. According to Rebbi Yochanan it is considered Adam ha'Mazik as if you caused the damage with your own hands.
2. The place where the coal landed is considered Tzeroros and therefore it pays Chatzi Nezek, but there is no Chiyuv for the rest of the grain because there is no Chiyuv for the Esh of an animal because Esh is only Chayav if it is the money of the Ba'al ha'Esh according to Reish Lakish.
3. The grain in the place that he put down the coal is Regel and the rest of the stack of grain is Tzeroros according to Rebbi Yochanan who holds that an Esh is like an arrow.
4. According to Reish Lakish it is only Chayav if the camel stopped near the store to relieve itself and since it was overloaded the flax protruded into the store and caught on fire and when it caught on fire the flax was pushed up against the entire store and set the whole store on fire. However, if the flax was not pushed up against the entire store even if the store burned down after the fire spread it would be Patur according to Reish Lakish because a person is not Chayav for the fire of his camel.
5. Since he is Chayav Misah for the death of the servant he is Patur for the damages. According to Reish Lakish he is only Chayav Misah for the death of the servant if he sets the fire directly on the servant.
Rebbi Yochanan holds that Esh is Chayav as if it was your arrow. The Nimukei Yosef asks according to Rebbi Yochanan why it is permitted to light candles before Shabbos. Since the fire is your arrow it is as if you are burning a fire on Shabbos. The Nimukei Yosef answers that it is regarded as if the entire act is done at the second that the arrow left your hand and the subsequent burning of the flame is not a significant act because if it was a significant act you could be Patur for that act because it is an Ones since it is too late to take it back.
AN OVERLOADED CAMEL
If a camel is overloaded with flax and the flax protrudes into a store and catches on fire and burns the store down the owner of the camel is Chayav whether the camel stopped or didn't stop because he should not have overloaded his camel. If the storekeeper left a flame outside the store and the flax caught on fire the storekeeper is Chayav to pay for the flax even if the flame is a Ner Chanukah because he is obligated to guard his flame. (Shulchan Aruch CM 418:12)