Tbh this sounds like an issue with understanding English to me.
With “state of being”, he means clauses that express that one thing is another thing. I’m not sure how you would even apply this to a verb. He’s talking about clauses like “N1 is an N2” or “N1 is not an N2” or “N1 was an N2” and so on. These clauses express a state of N1 being an N2 or not.
In this context, he’s introducing the ability to modify a noun with such a clause, for example starting with this:
猫は猫ではない The cat is not a cat.
We can turn the description of the cat into a relative clause by simply moving the description of the state of being in front of the noun:
猫ではない猫 A cat that is not a cat.
He is saying that this works with state-of-being clauses that are negative, in the past, or both, including ones that are less formal like じゃない for ではない. However, it doesn’t work with clauses like this that use the copula だ:
猫は猫だ The cat is a cat.
This can’t be turned into a relative clause in the same way; a clause that ends in だ can’t be used as a relative clause.
There are other ways to still do this but in this text, he’s talking about things that work and not explaining how to work around things that don’t.