My husband had the opposite happen- one day his mother, who does genealogy as a hobby, called him up. On a whim, she had looked up his father (they'd been divorced for over 30 years at that point), and discovered that he had died more than two years previously. Neither DH nor his sister had ever been notified. Obviously the family is estranged, but DH does wish that he knew how his dad died. The cause of death is listed as "heart failure" on the death certificate, and DH had no knowledge of any heart disease on that side of the family.
OP, what would make you happy? Would you like your relatives to contact you in case of a medical emergency? A death? Never contact you again? Once you decide what you'd like, then you can work on a way to request it. If you're happy knowing that they have the ability to contact you, but you're willing to leave it up to them what kind of emergency would require contact, then you're there already.
And whatever happens, don't let anyone tell you how to feel. Your feelings are your own, and although society would like us to believe that no matter what, anyone related by blood is faaaamily, and requires special treatment, there's plenty of evidence on this forum that family is the people who love you, and blood relatives may or may not be part of that group.