You would be giving up those rights--and only those rights--which the terms of the severnace agreement specifically say you are giving up. A severance agreement is a contract; and like any other contract, it is enforced according to its plain terms. So the key is to simply read the agreement carefully, and if you are not comfortable with it, don't sign it--not until it's been revised so you are only giving up those rights you are willing to give up.