The FAA keeps track of aircraft accidents, failures, and other problems, specific to individual makes and models. If the FAA sees a problem caused by a design or manufacturing fault on a certified aircraft it will issue an airworthiness directive (AD) and require that owners have the component inspected and, if needed, repaired.
ADs include part replacements on specific model aircraft. If you’re buying a used aircraft you need to know about any ADs issued for the craft and verify that the issues have been addressed. To find out what ADs have been issued on any plane you own or are buying, contact the FAA.
Manufacturers of the new LSAs issue “safety of flight” bulletins as needed to make sure all aircraft they produce continue to be airworthy. The FAA requires compliance with the bulletins but does not oversee their distribution or make sure they are complied with. It’s up to you to comply to assure the plane’s airworthiness, and it’s up to you to research the bulletins for any used aircraft you’re considering buying. Whether, as a private pilot, you fly a certified aircraft or a consensus (LSA) aircraft, it is up to you to make sure that it is airworthy under the appropriate rules.
"Man cannot discover new oceans unless he has the courage to lose sight of the shore."
-- Andre Gide