"While leaving the bank, Mike's watch was stolen."

"As he was leaving the store, Mike's watch was stolen."

I assumed both sentences were incorrect because "Mike" isn't referenced, only "Mike's watch" is. I am told, however, that the second sentence is correct. Can anyone explain, please?

can someone help please? thanks in advance

I believe both are incorrect..

Sentence 1 is incorrect but sentence 2 is correct.
It may be noted that sentence 2 is a clause-unlike sentence 1 which is a phrase.

I believe both are incorrect. The second sentence should be

As he was leaving the store, Mike had his watch stolen.

the first sentence is incorrect, because the logical predication suggests that mike's watch itself was leaving the bank. when you have a subjectless modifier that comes at the head of a sentence (such as the modifier here), it modifies the immediately following noun by default.

the second sentence is also "incorrect", because of an extremely obscure "rule" that we call "possessive poison". this "rule" (which i'm putting in scare quotes because most english language authorities don't even recognize it as a rule) states that a possessive noun can't serve as the antecedent for a pronoun. therefore, because "mike's" is possessive and therefore ineligible, "he" technically doesn't have an antecedent.
although the gmat writers obey this rule scrupulously - you won't find any official problems in which the correct answer violates it - it has NEVER been the deciding issue in a SC problem. in fact, we only know of one problem that even mentions it - #86 in the purple verbal supplement - in which the answer choice containing "possessive poison" can be eliminated by other means anyway.
this "rule" is treated in the current edition of the strategy guide. we're definitely going to scale down our treatment of the rule for the next edition, because we've given this rule too much attention in the current edition.

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note:
if the purpose of this forum is gmat study, then it's absolutely pointless to suggest "fixes" to sentences - because you don't have to "fix" sentences on the gmat. all you have to do is identify correct and incorrect language in already extant sentences, a completely different endeavor than trying to edit sentences.

nevertheless, if you insist on editing the sentence, the best edit is probably "as mike was leaving the store, his watch was stolen": just switch "mike" and the pronoun.

the edit suggested in the last post - "mike had his watch stolen" - isn't as good as the former one, because "had his watch stolen" seems to imply that mike actually set up the theft (intentionally); that's the usual meaning of "x had y done".