This question in inspired by this other one, which asks what is the theoretical lower mass limit for a gravitationally stable neutron star (not the Chandrasekhar limit which is the upper mass limit for a white dwarf, or the effective lower mass limit of real neutron stars that are formed in the universe, but how little mass one could form a gravitationally stable neutron star in theory). According to ProfRob's answer to it, it probably lies somewhere between $0.087$ and $0.19$ solar masses (computations differ, but this gives us an order of magnitude).
I would like to ask the exact same question about white dwarfs: is there a theoretical lower mass limit at which they are stable, and if so, what is it? Again, I don't mean the lower mass limit at which real white dwarfs are formed in the universe, I mean the lowest mass for which it could remain stable.
Or to put it differently, if we remove mass from a white dwarf, it is well known that its radius increases (roughly as the inverse cube root of the mass): how far down does this relation hold, and what happens if we keep removing mass? Does the star eventually break apart? Or do we encounter some kind of discontinuity as matter "de-degenerates"? Or does the star's matter simply continuously become less and less degenerate as we remove it? If the last is correct, what is the order of magnitude of the mass for which the radius would be a maximum (and which is arguably the point at which the star ceases to be a white dwarf)?
The answer might depend a lot on the star's composition and temperature, but I just want a ballpark figure, not a detailed analysis. (Say, maybe a cold/black dwarf made of carbon.)