They were sold to the sideshow at a very young age.
It was easy to see why -- the twin pig-faced girls could really draw a crowd. As they got older, they had to keep the audiences coming and so they developed an act -- singing, playing the accordion, finishing each other's sentences. When things became desperate, they upped the ante and wore a single dress and sold themselves as conjoined pig-faced twins.
Of course, in time, the truth became obvious. The owner of the side show was not only desperate, but he was very very nearsighted.