Is there any such thing as noun pronoun proximity?

Question

I have read of Concord (or noun-verb agreement) and was wondering if, is as I have been told, there is a similar grammar rule for noun-pronoun agreement/proximity.

When there's a sentence where two nouns are given and a pronoun used, to which noun will the pronoun be assigned?

1. Carol visited Mary. Mary is the lady living next door. She had barely eaten that day. Or
2. Carol visited Mary. Mary lives next door. She had barely eaten that day.

Are the above sentences even grammatical?

Assuming they are, I am tempted, in the first example, to assign the pronoun to the subject in the preceding sentence, but I'm not absolutely certain because I've heard that the pronoun(just as in noun-verb agreement) should be assigned to the noun closest.

3. Carol and Mary had been best friends for years. Until she got sick.

To who does the pronoun refer? Why? Is there any such rule as alluded?

Answer 1

The name of the linguistic principle that governs how pronouns are resolved to entities mentioned in the discourse is:

anaphora resolution.

Not all languages are identical in anaphora resolution, but the simplest rule is mostly universal, the closest preceding noun that matches number, gender, person, etc. Exceptions tend to start from this. (as to a literal answer to your question, no, there is no name for this rule. But 'anaphora resolution' is what you're talking about, it's the name for what any such rule is trying to do.

Answer 2

In your first two examples, "she" refers unambiguously to Mary, as the most recent possibility.

But in your third example, "she" could refer to either Carol or Mary, because "Carol and Mary" is a syntactic unit. In fact, I might go so far as to say that your third example is ungrammatical, almost like "Carol and Mary is sick".