According to her official Marvel Comics biography page, she can only change her volume, but not her mass. Therefore, there would be flesh that was cut off from her body lying on the floor where she was fighting Wolverine.
She wouldn't have to become left handed after this, as she could just shapeshift to keep her fingers, even though that wouldn't necessarily be the part of her that was cut off.
She would lose the mass in her body equivalent to the volume times the density of her body that she moved into those claws. So she would not be as dense as she was before, though in the grand scheme of things I don't think she'd have to worry about becoming incorporeal unless she lost a limb or something, and there's always the possibility of her giving up an inch out of her torso to maintain density for her mass.
Also, checking out the Marvel Wiki Page, she is noted to have enhanced regenerative capabilities, so any mass that she did lose, she could regrow in a vein similar to Wolverine's (though not nearly as efficiently). Though, this doesn't go to answer the main section of the question as to what happened to the parts that got cut off, this would explain the follow-up to why she wasn't left-handed later on.
According to the Official Handbook of the Marvel Universe (Corrections),
As such, her weight is no more variable than any person; she gains and loses it through eating, dieting and exercising.
So the flesh that was cut from her by Wolverine would be "lost weight". She could then eat enough to gain a pound (or whatever), then reconstruct her body back to normal.