Please use sentences written by native speakers, if possible. I can barely understand what you are after. He revived my dead dog.
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park sang joonHe revived my having died dog.This doesn't sound like an English sentence, and that is what CB was pointing out.
park sang joonMy dog having died, he revived it.This contradicts your original idea: "My dog had been dying little by little but it din't die yet before he revived it."
park sang joonHe revived my [having died] dog.If the dog had died, nobody could have revived it. "having nearly died" is, I think, the concept you want. So you're asking, in effect, if you can use a structure like
park sang joonShouldn't I use such sentences as the above sentence?It's good practice for learning English grammar, and it may help you to understand written English, particularly if it was written quite a long time ago, but it won't do you any good in a conversation.