Do you mean how was their slave status decided? The law settled on a pretty simple, direct system. If your mother was a slave, you were a slave. It didn't matter if you mother had all of one black great-grandparent (or less), you inherited her slave status even if you were so pale you could misplace your hands in a snowstorm. If your mother subsequently became free, that did not inherently emancipate any children. Physical appearance didn't really enter into it. Here's a picture of some slaves with a variety of skin tones.

Ellen Craft was light-skinned enough that she successfully posed as a white man and got herself and her husband William up to Boston and freedom by pretending he was her slave valet. The disguise was good enough that when she shared a railroad car with some southern belles and their father, she got invited to come calling at their home next time she was through Virginia.

The Craft's narrative includes the story of a woman, Salomé Miller in Louisiana who claimed she was a German wrongly enslaved and managed a successful freedom suit. But that suit was decided on the grounds that she was white racially, not by skin tone, and therefore free. They also include one about a white boy who was kidnapped from Ohio and somehow had his skin stained and was sold as a slave. That said, we should probably read both of those stories with caution. The Crafts didn't have firsthand knowledge of either case and the second seems especially unlikely. Kidnappers had far easier prey in the North than random white kids in the form of free blacks.

The system could get grimly comical. William Freehling relates in Road to Disunion, Volume One, that in Charleston, whites couldn't tell the difference between a tanned white person and a light-skinned black person. They thus required biracial people to wear black veils to remove the ambiguity. He doesn't say how thoroughly this was enforced, though.

There is already a post Here about it that seems pretty solid.

Basically they were treated the exact same as any other slave.