"And it eat in another's field" — Rabbi Nathan addressed a scenario where someone stacked grain in another person's field without permission. If the field owner's beast then came out and damaged the grain, one might think the field owner is liable under the general law of "he sent his beast" into another's property.
The Torah prevents this by specifying "and it eat in another's field." The damage must occur in a field that belongs to someone else. But when a person stores grain on someone else's property without permission, the field remains the owner's property — it is not "another's field" with respect to the field owner. The grain-stacker has no legal right to be there.
Therefore, the field owner is not liable when his own animal eats grain that was stored on his property without his consent. The intruding grain-stacker assumed the risk by placing his property in someone else's domain. The Torah protects property owners from liability created by uninvited guests.
Rabbi Nathan's ruling establishes an important principle: the law of animal damages presupposes that the damaged property is legitimately located where the damage occurs. If you put your goods in my field without my permission, my animals eating your goods is your problem, not mine. The Torah's phrase "another's field" implicitly requires that the damaged party had a right to be in that field in the first place.