This is false. If a company makes you sign a statement that you are quitting instead of being fired as a condition of getting severance, they are committing unemployment insurance fraud and are subject to civil and criminal sanction in most states.

(The point of trying to make employees do this is to avoid claims against the company's unemployment insurance account in the state. How UI works differs from state to state, but in all instances claims against UI increases the company's ongoing UI expense.)