Drug resistance is a long-standing economic, veterinary and human health concern in human and animal populations. Efficacy of prophylactic drug treatments targeting a particular pathogen is often short-lived, as drug-resistant pathogens evolve and reach high frequency in a treated population. Methods to combat drug resistance are usually costly, including use of multiple drugs that are applied jointly or sequentially, or development of novel classes of drugs. Alternatively, there is growing interest in exploiting untreated host populations, refugia, for the management of drug resistance. Refugia do not experience selection for resistance, and serve as a reservoir for native, drug-susceptible pathogens. The force of infection from refugia may dilute the frequency of resistant pathogens in the treated population, potentially at an acceptable cost in terms of overall disease burden. We examine this concept using a simple mathematical model that captures the core mechanisms of transmission and selection common to many host-pathogen systems. We identify the roles of selection and gene flow in determining the utility of refugia.