happens to the eggshell though

absorbed, at least in cases where a shell is formed at all, some animals like this just have yolk. it's a few grains from placenta and continuously nourishing an embryo though, the yolk can run out and they wee thing gets out or they'll switch to eating other eggs or uterine secretions.

because argonians are presumably one species (naga are questionable) the switch to live-birth shouldn't be too "advanced", probably just weak-shelled eggs and no uterine action after the yolk is spent. infant mortality in places like skyrim is probably pretty high.