Adding more solid to a solid/gas equilibrium $$\ce{CaCO3(s)&lt;=&gt; CO2(g) + CaO(s)}$$  

In this equation, what happens if you increase the amount of one of the solids while there are existing quantities of everything else? 

According to the calculation for the equilibrium constant, equilibrium is only dependent on the concentration of $\ce{CO2}$, so it technically should not change anything, right? However, if you decrease the pressure of the $\ce{CO2}$ enough, then shouldn't there be a point where the equilibrium constant can no longer be met because there aren't enough moles of $\ce{CO2}$?

Additionally, at this point, shouldn't adding more $\ce{CaCO3}$ change the point of equilibrium?
The concentrations of the solids change only negligibly with temperature or other reaction conditions and so are involved in the equilibrium only as constants. The amount of solids present does not change the concentration of each solid in its crystal structure. Therefore the equilibrium of the reaction is written as:  

$\mathrm{K = constant}\times \ce{[CO2]}$ 

If one of the reactants ($\ce{CaCO3, CaO, CO2}$) is not present, there is no equilibrium.