Are there rules about the subject of a subordinate clause?

The following two sentences, which is commonly used and grammatically correct?

1. When Lisa unwrapped the package, she found the cellphone inside it was broken.
2. When she unwrapped the package, Lisa found the cellphone inside it was broken.

I know the noun Lisa is the antecedent of the pronoun she. Are there any specific rules about the subject of a subordinate clause? How about if we put the subordinate clause after the main clause?

The basic rule for pronoun coreference was explicated by Ron Langacker in his classic 1969 paper "Pronominalization and the Chain of Command"¹.

It's stated succinctly in terms of the syntactic structural relationships precede and command. One of these terms is obvious, but the second isn't.

1. Precede means 'precede in the utterance'; it refers to time.
   So, in The boy lost his hat, the noun phrase the boy precedes the possessive pronoun his.
   That's the norm; ordinarily, the antecedent noun phrase comes before any pronoun that refers to it.
   That's what antecedent means in Latin, in fact -- 'coming before'.
   It's what we expect. But it's not what always happens.

2. Command is not a temporal relation, however.
   Where precedence is linear, command is vertical. It refers to clause structure. An item in the main clause commands everything in clauses subordinate to it.
   An item in a subordinate clause does not command anything in a clause above it. And items in the same clause command each other.

The rule is very simple to state, since it's negative, like most rules:

• A pronoun may not both precede and command its antecedent.

So, in the examples given (leaving out irrelevant details)

• When Lisa unwrapped the package, she found the cellphone inside.
• When she unwrapped the package, Lisa found the cellphone inside.

the first one has the antecedent preceding its pronoun, as we expect. In the second, however, the pronoun precedes its antecedent grammatically, because it's not commanding it. Let's look at the other possibilities. Note that the subordinate clause about unwrapping can appear either before or after the main clause; adverbial clauses are like that:

• Lisa found the cellphone inside when she unwrapped the package.
• *She found the cellphone inside when Lisa unwrapped the package.

Only one of these is grammatical. That's the first one, with the antecedent preceding and commanding the pronoun, so that follows the rule.

The ungrammatical sentence is the one in which the antecedent Lisa occurs in a subordinate clause, after the main clause, and the pronoun she occurs in the main clause, before the subordinate clause containing Lisa. In other words, the pronoun she precedes its antecedent Lisa, and it commands Lisa (since Lisa occurs in a subordinate clause and she occurs in the main clause) and that violates the rule.

Note that this is not a rule "about the subject of a subordinate clause". This is a rule about pronoun coreference, which happens to apply to the subject of a subordinate clause, but could apply anywhere to any noun phrase. So anybody looking for this answer won't find it by searching titles.

Remember, you asked.