"Mama Parappa" (no official name has been revealed) is the mother to Parappa Rappa and Pinto Rappa, yet a very obscure character hardly -if ever- present in the fiction, presumably because she would be occupied by her work. Her absence is glaring and sometimes comes off as if she has passed away.
In a the RodneyFun Comics, PaRappa has gotten quite a gaming habit. His mother -dressed up in Firefighter suit- and his father are drinking tea together discussing PaRappa's situation. They are shown to be worried and ponder if he should get a job, which PaRappa overhears and acts on.
In PaRappa The Rapper, she is mentioned by an imaginative PaRappa Papa in one of PaRappa's dream sequences. As PaRappa had just lended and destroyed his dad's car, he imagines how his dad would react to this news. "What do I tell your mother?"
In Um Jammer Lammy, the background of Stage 2 with Chief Puddle is the dancefloor to one particular firefighter who strikes resemblance to PaRappa's mother from the comics and is most likely intended to depict her, as she is also a firefighter. As far as her fellow firefighter colleagues seem to care about the situation at hand, she seems to care the least, even having her jacket unbuttoned for the occasion.
In PaRappa the Rapper 2, when trying to find a solution for the noodle problem, Papa PaRappa is a bit unfocused and finds a photograph of him and his wife on their honeymoon. He seems euphoric seeing it again, looking back on good memories and utters that "she used to be so nice." PaRappa's reaction is in sync with his father. The photograph is never shown to the audience.