Negative Capacitance in Ferroelectrics From the Devonshire theory of ferroelectrics we can obtain Polarization vs. Electric Field curve at a given temperature.

From the graph it can be seen that a portion of the curve has negative slope which can lead to the negative capacitance(negative permittivity) but cannot be achieved in real capacitance measurements due to instability of the ferroelectric in this region. It is said that this region can be stabilized by adding another linear dielectric capacitor in series with the ferroelectric capacitor such that the overall capacitance of the system becomes positive. My question is how does the addition of another series capacitor stabilizes the system and what actually happens at the domain level in the ferroelectric during that negative slope region.
 A: You question is a bit unclear.  The red region of the P-E diagram that you show comes from the equation for Gibbs free energy in a ferroelectric, with the electrostatic term:
$G= \frac{1}{2}  \alpha_{1}  D^{2} +\frac{1}{4}  \alpha_{2}  D^{4}  +\frac{1}{6}  \alpha_{3}  D^{6}-E*D$
Taking the derivative with respect to D:
$\frac{ \partial G}{ \partial D}=\alpha_{1}  D +\alpha_{2}  D^{3}  +  \alpha_{3}  D^{5}-E$
Solving for the minima:
$E=\alpha_{1}  D +\alpha_{2}  D^{3}  +  \alpha_{3}  D^{5}$
Plotting E as a function of D, and reflecting the graph over the D-E axis, reproduces your image, however, the system never exists in the red region you show.  If it did follow the blue-red-blue curve, the system would not exhibit hysteresis, and hence not be ferroelectric.
Because the system never exists on the curve where the red is shown, the capacitance $\frac{ \partial D}{ \partial E}$, can't be calculated (or measured) there.  Instead, capacitance of a ferroelectric shows a different type of hysteresis loop, as shown here:

Note, that although the capacitance varies significantly, and exhibits hysteresis, it is never negative.
Your comment regarding adding a linear capacitance in series with a ferroelectric capacitor is in accordance with Kirchoff's Law for capacitors; the inverse of the total capacitance is equal to the sum of the inverses of the individual capacitances.
