Me going to a strip club can ruin my social image.
My going to a strip club can ruin my social image.
Well I guess that isn't actually the case. I think using possessive or pronoun actually depends on the sentence itself . For example I want to see you smiling ... I want to see your smiling. This doesnt make sense. However i want to see your smiling face does. Similarly I want to hear you singing (here in possessive it means I want to hear you while singing) . I want to hear your singing (here singing is a noun). So they both are right. But have different meanings