Three-body recombination in quantum gases is traditionally associated with heating, but it was recently found that it can also cool the gas. We show that in a partially condensed three-dimensional homogeneous Bose gas three-body loss could even purify the sample, that is, reduce the entropy per particle and increase the condensed fraction $eta$. We predict that the evolution of $eta$ under continuous three-body loss can, depending on small changes in the initial conditions, exhibit two qualitatively different behaviours - if it is initially above a certain critical value, $eta$ increases further, whereas clouds with lower initial $eta$ evolve towards a thermal gas. These dynamical effects should be observable under realistic experimental conditions.
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