I'll try to explain this one...
There is no such recognized board certified specialty or specialty certification as "breast surgery" in the books of the ABMS (the generally recognized body that acknowledges boards). However, there are a number of general surgeons who do consider themselves breast surgeons in that they limit themselves to breast surgery in their practice. A few of them have even taken specific training in breast disease (generally focusing on the multidisciplinary aspects of breast disease, since from a technical perspective, 95+% of breast cases can be done by a third year resident of below!). Some of them got there by way of general surgery, some finished general surgery then did a surgical oncology fellowship to follow (a 2-3 year fellowship, as specified by the society of surgical oncology (SSO)). Keep in mind that there is no board of surgical oncology either.
Does this mean that they are not specialists? no. But at the same time, they show up in the masterfile as a "general surgeon."
As far as who would hire a general surgeon, if my mail from recruiters is any indication, there are a ton of general surgery jobs out there. Some allow you to focus on one aspect or another of general surgery, but the vast majority are looking for surgeons that take care of any kind of patients. Sure the vast majority of cases in community practice are cholecystectomy, hernia, and breast cases, but there are plenty of community surgeons I know doing pancreatic and liver work, bowel work, and even the occasional vascular procedure.
Don't let people fool you, general surgery is alive and kicking. It faces the challenge of super-specialization that all specialties face at the large academic centers, but outside of that, the field still needs those that want a broad practice.