They can't make him give up the right to paternity leave (unpaid leave) under FMLA IF he and his company qualitfy for FMLA (see below), since a private agreement cannot overrule the law; therefore, an agreement to give up his paternity leave rights under FMLA would be void as against public policy and the law, and if they terminated or otherwise punished him for not agreeing to this, he would have a legal claim.However, he would have to be able to take paternity leave under FMLA: his company must have 50 or more employees locate within a 75 mile radius, he must have worked there at least 12 months and he must have worked at least 1,250 hours during the past 12 months.If he is not eligible for FMLA, they can make him agree to not take paternity leave, since without FMLA eligibility he has no right to paternity leave.They can also make him agreee to not take time off for a death in the family, since there is no legal right to bereavement leave.