► We study K-type asteroids which form a ‘halo’ around the Eos family. ► We explain its origin as bodies escaping from the family ‘core’. ► Major processes are the Yarkovsky effect and interactions with resonances. ► Our N-body model allows us to estimate the age of the family 1.5–1.9Gyr. We study K-type asteroids in the broad surroundings of the Eos family because they seem to be intimately related, according to their colours measured by the Sloan Digital Sky Survey. Such ‘halos’ of asteroid families have been rarely used as constraints for dynamical studies to date. We explain its origin as bodies escaping from the family ‘core’ due to the Yarkovsky semimajor-axis drift and interactions with gravitational resonances, mostly with the 9/4 mean-motion resonance with Jupiter at 3.03AU. Our N-body dynamical model allows us to independently estimate the age of the family 1.5–1.9Gyr. This is approximately in agreement with the previous age estimate by Vokrouhlický et al. (2006) based on a simplified model (which accounts only for changes of semimajor axis). We can also constrain the geometry of the disruption event which had to occur at the true anomaly f≃120–180°.