Here are some grammatically correct ways to express this in French:
* Elle ne pourrait jamais vivre sans toi. (This is the most literal translation and is grammatically correct)
* Elle ne vivrait jamais sans toi. (This is a more poetic way of saying it)
* Elle ne pourrait pas vivre sans toi. (This is a less formal way of saying it)
The sentence you provided is a bit awkward because it uses the double negative "ne...pas" which is unnecessary in this context.