Ever wonder why toxic leaders sometimes don’t get fired for mistreating underlings? It’s because, in the short term, they can appear very effective, new research suggests.

People who work for highly toxic bosses—managers with more than a handful of bullying or undermining behaviors—tend to be more engaged in their work than other employees, according to a survey of 1,000 college-educated U.S. employees. The study, conducted by consulting firm Life Meets Work, also found such employees stayed an average of two years longer...