If I waive coverage now and suddenly lose coverage after open enrollment ends, will I be able to enroll in medical coverage through the City later?

Yes, loss of coverage is a qualifying event, contact Human Resources as soon as you learn you will lose coverage, and they can assist with your enrollment. Remember you will have 60 days to enroll in benefits from the date you lose coverage, but if you contact Human Resources early you may be able to avoid a gap in coverage.