I understand that Heckman selection models attempt to address selection bias by running two-part models. In the oft cited example of determinants of wage offers: 1) we have a group of people who work and do not work due to various reasons, 2) we only have wage offers for those who are working, and 3) there may be unobserved forces that drive people to work versus not work that may also impact wage offers.
My question is, what if we are only interested in the subgroup of people who are working? Does the potential for selection bias still apply since we are not interested in determinants of wage offers for both working and not working people? Why can't we just restrict to the population of working people, so long as this is the only group we are interested in?