No vaccine provides perfect protection, and so-called breakthrough infections after coronavirus vaccination are rare. Federal health officials have told fully vaccinated people they no longer need to wear masks or maintain social distance because they are protected, nor do they need to be tested or quarantine after an exposure, unless they develop symptoms. Now, the Centers for Disease Control and Prevention has stopped investigating breakthrough infections among fully vaccinated people unless they become so sick that they are hospitalized or die. Earlier this year, the agency was monitoring all cases. Through the end of April, when some 101 million Americans had been vaccinated, the C.D.C. had received 10,262 reports of breakthrough infections from 46 states and territories, a number that was very likely "a substantial undercount," according to a C.D.C. report. On May 1, the agency decided to investigate only the most severe breakthrough infection cases, while still collecting voluntary reports on breakthrough cases from state and local health departments. The agency will carry out vaccine effectiveness studies that include data on breakthrough cases, but only in limited populations, such as health care workers and essential workers, older adults, and residents at long-term care facilities. But even relatively mild cases of Covid-19 can lead to persistent long-term health problems, and it will be difficult to know the full scope without tracking mild infections as well.