Many wear processes used for modeling accumulative deterioration in a reliability context are non homogeneous Lévy processes and hence have independent increments, which may not be suitable in an application context. We here suggest to consider Lévy processes transformed by monotonous functions, which allow to overcome this restriction and provides a new state-dependent wear model. These transformed Lévy processes are first observed to remain tractable Markov processes. Some distributional properties are derived. The impact of the current state on the future increment level and on the overall accumulated level is investigated from a stochastic monotonicity point of view. Positive dependence properties and stochastic monotonicity of increments are also studied.