If I understand what you want to do, it is not really a statistical issue per se. As I understand it, you have a map of piecewise-constant areal population density (i.e. $\frac{\text{people}}{\text{area}}$), defined by a set of polygons.
So consider a particular polygon $A$ with density $\rho$ and population $N=\rho|A|$, where $|A|$ is the polygon area.
So to add a new polygon $B$, you first compute $C=A\cap{B}$, $A'=A-C$, and $B'=B-C$. If you intend that the populations in the overlap area are independent*, then $N_C=(\rho_A+\rho_B)|C|$. You would then subtract these contributions from the residual polygons, i.e. $N_{A'}=N_A-\rho_A|C|$ and $N_{B'}=N_B-\rho_B|C|$. Note that the densities of the residual polygons are unchanged, $\rho_{A'}=\rho_A$, $\rho_{B'}=\rho_B$.
*This is one interpretation of the example you gave where $B=C$ so $B'=\emptyset$. If the overlap-populations are not independent, then this would be double counting! This is the part that is not clear to me from your description.
Update: Based on the clarification, the assumption $\rho_C=\rho_A+\rho_B$ is not appropriate.
So then the uncertainty all boils down to how you estimate $\rho_C$. (The assumption $\rho_{A'}=\rho_A$ and $\rho_{B'}=\rho_B$ still seems valid.)
I am not sure if there is a "correct" answer here (but hopefully someone chimes in, if there is!).
A reasonable approach is to model the density in the overlap as a weighted average of the component densities
$$\rho_C\approx\frac{w_A\rho_A+w_B\rho_B}{w_A+w_B}$$
One possible approach for weighting could be based on the relative area of a component to the overlap, i.e.
$$w_A=\frac{|C|}{|A|}\,,\,w_B=\frac{|C|}{|B|}$$
This captures the idea that if $|A|\gg|C|$ and $|B|\approx|C|$, then $\rho_C\approx\rho_B$, which seems close to your example qualitatively.
(Note that $|C|$ could be omitted from the weights here, as the constant factor will cancel out.)
