Accelerated failure-time regression models with an additional regression model for the surviving fraction are proposed for the analysis of events that may never occur, regardless of censoring, for some people in the population risk set. The models attempt to estimate simultaneously the effects of covariates on the acceleration/deceleration of the timing of a given event and the surviving fraction; that is, the proportion of the population for which the event never occurs. The extended family of the generalized Gamma distribution is used for the accelerated failure-time regression model; the logistic function is used for the regression model of the surviving fraction. The models are applied to the data of interfirm job mobility in Japan to assess variability in “permanent employment” among white collar and blue collar employees in firms of different sizes, independent from their variability in the timing of interfirm job separations.