Chimeraism and Fetomaternal microchimerism.
http://en.wikipedia.org/wiki/Chimera_(genetics)
The latter is (most commonly) where maternal cells live and reproduce in the child. This is apparently very common.
Chimerism is where:
In zoology, a chimera is an animal that has two or more different populations of genetically distinct cells that originated in different zygotes; if the different cells emerged from the same zygote, it is called a mosaicism. Chimerism is rare in human beings: there have been only about 40 reported cases.
The difference in phenotypes may be subtle (e.g., having a hitchhiker's thumb and a straight thumb, eyes of slightly different colors, differential hair growth on opposite sides of the body, etc) or completely undetectable . Another telltale of a person being a chimera is visible Blaschko's lines.
Recent studies of tortoiseshell male cats and unusually coloured tortoiseshell-like cats suggest that natural chimerism is far more common than previously realised and that it frequently goes undetected.
A famouse Chimera case is that of Lydia Fairchild. She was arrested on kidnapping charges when genetic testing showed she could not be the mother of her kids. Genetic testing of her reproductive organs DID match.
http://en.wikipedia.org/wiki/Lydia_Fairchild