People make alminated blades with carbo steel center and stainless on each side. Inever understood this as what I worry about is cutting edge [center layer ] which should be stainless not the less critical outsides.
The reason people will put the stainless on the flats and primary bevel is so the majority of the blade is relatively easy to care for, in terms rust prevention and maintenence.
While the carbon steel core, showing in the very bottom part of the primary bevel, secondary bevel and cutting edge will still need to have some precautionary measures taken in regards to care. That being said, carbon steel is used as the core because it, generally speaking, can be hardened to a higher RC, is more stable with a finer edge angle, and can be sharpened to a more refined edge.
If they had a softer stainless core wrapped in a carbon jacket, it would serve no purpose. The stainless edge would dull faster, unless it was a Really higher end, fine carbide steel, m390/s110v/s125v. Though even then you would only get a toothier edge as it wore, not a smooth, polished edge that produces a Really smooth slicing edge that requires a maintenance a little more frequently via a strop. All the while, needing More maintenance due to it being jacketed in carbon steel which will patina and rust if not cared for correctly.
This is all speculation addressing others responses.
OP: Did you mean a laminated blade like they assumed, or a forged, pattern welded, damascus style blade?
Damascus or more accurately, pattern welded steel is a mixed steel of sorts. Generally mixed of higher and lower Nickel, chromium, or other materials, that will etch at different rates or near not at all, if a stainless steel was used in the mix.
I get that it may be perceived as a more corrosion resistant way to have nice carbon steel edge, but a corroded edge is a problem. Just an easier one to fix.
What I don't understand is why no one talks about the carbon migration problem when you weld high carbon to low.
When creating a damascus styled, pattern welded blade, the carbon migration is somewhat mitigated due to the fact that the different steels used will wear at different rates along the cutting edge. This in turn is creating a very toothy cutting edge, one that can often be felt by running your fingernail down it. The ridges and valleys will sometimes feel like a hill, climbing and falling, sometimes they will be sheer and abrupt.
So while some of the carbon will bleed from the higher % to the lower, it isn't really enough to be noticed, at least not in the shadow of the more visable effects on how the blade is "feels" in hand.