1) No, your employer may NOT make you give you up your right to unemployment. Your right to unemployment is set by law, and no contract that contradicts or tries to override law is valid, and you cannot be made to give up this statutory (set by statute) right. You can't be required to sign anything like this, since it is an illegal agreement.2) Bear in mind that under the law, if you quit, resign, or are fired "for cause," you will not receive unemployment; you get unemployment if terminated other than "for cause." "For cause" terminations are for things like insubordination, violating company policy, and unauthorized absences (also for committing crimes of various kinds at work or acting to sabotage your employer in some way). There is NO right to miss work to pick up your chidren from school due to sickness or to have to stay home with your children when they are sick, unless the employer is covered by, you are eligible for, and the situation warrants unpaid leave under a family leave law. Your state does not have its own family leave law, which means the only one that may apply is the federal Family and Medical Leave Act or FMLA. That only applies if 1) your employer has at least 50 employees located within a 75-miles radius; 2) you have worked there at least a year and worked at least 1,250 hours in the past 12 months; 3) you are using the leave for medical care of yourself, a spouse, a child, or parent; and 4) the reason for the medical care is a *serious* medical condition--upset stomaches, colds, the typical case of the flu, headaches or earaches, etc. do NOT qualify.Therefore, if you miss work for medical causes for everyday ailments of yourself or children (non-serious conditions), whether or not you have a doctor's note, or miss work simply because you don't have childcare to pick up or watch your child, you MAY be terminated for cause unless you used paid time off (PTO, like sick or vacation days) you earned. There is no right to miss work, even to take care of your children or if you are not feeling well, without using FMLA or PTO, and being terminated for unuathorized absences is a termination "for cause" that will deny you unemployment under the law.