The Bach-Peters Paradox

Pronouns refer to nouns. In the sentence Francis touched the beggar and cured him, we can “unpack” the pronoun him by replacing it with its referent, the beggar: Francis touched the beggar and cured the beggar.

But what if a sentence has two phrases that refer to each other? The pilot that shot at it hit the Mig that chased him. Now there’s an infinite regress:

The pilot that shot at the Mig that chased the pilot that shot at it hit the Mig that chased the pilot that shot at it.

It seems that no amount of unpacking can resolve these pronouns. Yet most readers can understand the sentence immediately. How are they able to do so?