If something is slowly and secretly causing harm, it's insidious — like the rumors no one seems to listen to until suddenly someone's reputation is ruined.
Insidious is related to the Latin noun, īnsidiae meaning "ambush" which comes from the Latin verb, īnsidēre "to lie in wait for." This is very fitting as an insidious rumor or problem is one whose negative effect is not realized until the damage is already done. Similarly, an insidious disease develops internally without symptoms, so that you don't realize right away that you are sick.