Motivated by the success of preprocessing in Boolean satisfiability (SAT) solving, development and analysis of preprocessing in maximum satisfiability (MaxSAT)—the optimization extension of SAT—has received noticeable attention recently. The correctness of preprocessing techniques for MaxSAT is standardly established by arguing that optimal solutions are maintained. However, the effects of preprocessing on the relative perceived costs of non-optimal solutions has not been considered, despite the fact that one of the most recent directions in MaxSAT research is developing incomplete solvers, i.e., solvers that are designed to provide good (but not necessarily optimal) solutions fast. In this paper, we bridge this gap by showing that employing central preprocessing techniques misleads MaxSAT solvers in terms of their interpretation of the costs of non-optimal solutions seen during search. This issue impacts both complete and incomplete solvers and the effects can be shown to be present also in practice with different types of MaxSAT solvers. Furthermore, we propose ideas for circumventing these negative effects in the context of stochastic local search algorithms for MaxSAT.