This is always the case with bracketing commas, and it gives you a simple way of checking your punctuation. If you have set off some words with a pair of bracketing commas, and you find you can't remove those words without destroying the sentence, you have done something wrong. Here is an example of wrong use, taken from Carey (1958):
*Yet, outside that door, lay a whole new world.
If you try to remove the words outside that door, the result is *Yet lay a whole new world, which is not a sentence. The problem here is that outside that door is not an interruption at all: it's an essential part of the sentence. So, the bracketing commas shouldn't be there. Just get rid of them:
Yet outside that door lay a whole new world.
Is this a common rule?
**In this example from a published review the isolated information does damage the sentence when removed and or leaves something ungrammatical.* * Is there any right or wrong in this? It looks and sounds wrong to me eitherway. I think the sentence should flow when the information is removed.
[It] faithfully adopted much of what so resonated in the original genre-creating film, the stoic killer, the gruesome executions, the suburban nightmares, what makes his version such a thrill is how it deviates from its long-ago predecessor.