Literally: not – sick – stop – disaster
Alternately: To be healthy.
Notes: 息 primarily refers to “breath,” but has been associated a variety of words (cf. 息子 – musuko – “son”), and in this case refers to stopping something. The term 息災 on its own is Buddhist in origin, and refers to the power of the Buddha keeping someone free of disease, but the “breath” connection seems to be related to terms like 休息 (kyuusoku – “rest/relaxation”) as in catching one’s breath.
An apparently-related compound replaces the 無 with 一 (ichi), arguing that someone with a (non-terminal) illness is likely to take better care of themselves than someone effortlessly healthy, and so in the end, people with imperfect health will actually live longer.