There is NO obligation to pay severance whatsoever, unless and only if you already had a written contract guarantying you severance. (If you did, the company has to do or pay whatever the contract says; if it doesn't, you could sue for breach of contract.) Since severance is completely optional and voluntary for the company, the company has the right to set any restrictions or requirements it likes on it, such as requiring you to work until a certain date to get your severance, since the alternative is, they could have simply laid you off without any severance.