A number of pathogens cause chronic infection in survivors of acute disease and this is believed to be a common means of persistence, including for highly virulent agents. We present a model in which transmission from chronically infected hosts causes chronic infection in naive individuals, without causing acute disease - indeed 'protecting' against it. Thus the pathogen obtains the benefit of virulence (high transmission rate), but mitigates against the cost (high host mortality). Recent findings suggest that rabbit haemorrhagic disease virus (RHDV), a highly contagious and virulent pathogen, may also utilize this alternative, 'avirulent', mode of transmission. The model may resolve the paradox of how RHDV can be highly prevalent in some populations, in the absence of mortality. Differences in host demography determine whether avirulent transmission prevents large-scale mortality (as in most UK populations) or not. Other pathogens may exhibit similar behaviour and the implications for emerging diseases in general are discussed.