The successful spread of a virus in a specific ecological niche is largely determined by host availability. The lower the host density, the longer the virus spends in the external environment between successive infections, thus increasing its probability of degradation due to physical and chemical variables, which ultimately could lead to its extinction. Nevertheless, the high error rate of viral replication, particularly in the case of RNA viruses, can lead to the emergence and subsequent selection of mutants that increase their probability of transmission under unfavorable conditions. This fact could cause some containment measures, such as those based on restriction of contacts, to have unexpected consequences that it is important to analyze. Whereas it is quite difficult to implement this kind of studies during the spread of real epidemics, evolution experiments carried out with controlled variables in the lab can be very useful to unveil regularities in virus behavior that allow to anticipate difficulties. In this work we have carried out an evolution experiment in which the bacteriophage Qβ, a virus with an RNA genome, has been propagated at different host densities under conditions that prevent the selection of defense mechanisms in the bacteria. Our results show that there is a minimal host concentration that separates sustained propagation from extinction. After a certain number of generations, all lineages propagated at suboptimal host concentration selected a mutation in the minor capsid protein whose phenotypic effect was to enhance the entry of the virus into the cell. Although it is difficult to extrapolate our findings to more complex situations, they show the need to carry out an exhaustive monitoring of viral evolution when measures based on confinements or physical barriers that limit transmission are applied.