The sentence in question
- I can't prevent your being offended.
is certainly grammatical, and, as @Billj points out, it's grammatical whether or not the subject of being offended is you or your. So that's one of the questions answered. Forget Google Docs and Grammarly; they're not competent at English grammar, let alone authoritative.
The other one is whether "being is functioning as a gerund here." Being is an auxiliary verb in the present participle verb form (the one that's inflected with {-ING
}), and it's followed by the predicate offended, which is the main verb of the clause, and in the past participle verb form (the one inflected with {-EN₁
}). A form of be is required as an auxiliary verb for both the Passive construction
- He was offended by the show, but he calmed down quickly
and a predicate adjective
- He was never happy, always offended; he died of terminal glowering.
In this case, you can't tell the difference, and it doesn't matter anyway, since be is the auxiliary either way.
The form of being does make a difference, though. It's not correct to say that being is a gerund. Gerunds are clauses, not words. So the question should be whether the whole clause is a gerund clause.
Even though some might say this isn't a gerund, I would. English gerunds are complement clauses with certain characteristics.
(Incidentally, I use the word complement only for argument noun clauses;
always clauses, always noun clauses, always argument nouns. That's my usage.)
They're one of four English complement clause types:
- Gerund (untensed)
- Infinitive (untensed)
- That-clauses (tensed)
- Wh-clauses (tensed)
The gerund construction is marked by one of two Complementizers, called
- POSS-ing (which means "Possessive subject plus {
-ING
} verb form", like your being offended)
- ACC-ing (which means "Accusative subject plus {
-ING
} verb form", like you being offended)
Either form is correct, and yes, you can call the whole clause your being offended a gerund clause, if it matters to anyone. Though it's incorrect to say that being is the gerund here -- being is only the verb that bears the {-ING
} gerund complement marker. The whole clause is the Gerund, and the whole Gerund clause is the direct object of the main verb can't prevent.