If a rare species receives more pollen from a crop than its own kind of pollen, either outbreeding depression or genetic assimilation can be an important problem. Depending on the parent, hybridization can drastically reduce fitness.
Genetic assimilation is an other problem if hybrids are fully fertile and vigorous.
A substantial pollen flow from a common crop could dilute the genetic integrity of a rare natural species up to the point where the rare form could be effectively assimilated into the crop species. In essence, the rare species can be hybridised out of existence. This scenario could well be real in the case of alfalfa in Switzerland, where Medicago falcata is presumably under heavy genetic pressure of Medicago sativa and its hybrids . The significance of this event would depend on the nature of the transgene product, whether the transgene is expressed, and the fate of the crop, that is, whether it was to be consumed by humans or animals or used for some other purpose.