We study a coupled system of ODEs which is non-explicit but subject to certain natural conditions. The aim is to describe the dynamics of a population subject to "assimilation pressure" from a larger system. We identify conditions for survival/extinction for the minority, and describe the asymptotic form of the dynamics, including a temporal power-law decay at criticality. We also describe the "offsetting effect", i.e. the presence of a transient peak of the majority population in a range of parameters. The overall conclusion is that the dynamics of the small population is principally governed by the resilience of its "last Mohicans".