Your implicit expectation that it is possible to uniformly typeset the closure of any piece of formula results from mistaking TeX for a markup system while it is a typesetting system. Often enough, you can ignore the distinction between these two concepts, which is made especially blurry by LaTeX. But when it comes to typesetting maths, it is not possible to assume that both concepts are the same (see how MathML distinguishes presentation and semantics).
To solve your problem, add near the definition of \cellFluid a new definition for a macro \cellFluidBar typesetting the closure of \cellFluid.
Alternatively you can look for alternative notations for the closure, such as $\mathop{\mathrm{Adh}}_X Y_0$, that are cumbersome but smooth that edge between markup and typesetting.
If you enjoy programming TeX, you can devise a \closure macro taking a unique argument and typestting its closure in a generic way but supports a dictionary of exceptions. Aside from fun, there is probably very little benefits over the first, easy and straightforward, solution.
\bar\cellSolidwill only put the bar on the Y, not the Y with subscript.$\overline{\cellSolid}$produce the desired result?\overlineextends over the index as well. And even on its own, it's much wider than\bar, so it looks wrong.\overlinefor closures,\barbeing too short. If a set is calledY_0I would want the line to go over the whole symbol pair, to distinguish from a "0opertaion" on the closure. Thus I think Jubobs suggestion is the correct one.