  We consider a probabilistic formulation of a singular two-phase Stefan
problem in one space dimension, which amounts to a coupled system of two
McKean-Vlasov stochastic differential equations. In the financial context of
systemic risk, this system models two competing regions with a large number of
interconnected banks or firms at risk of default. Our main result shows the
existence of a solution whose discontinuities obey the natural physicality
condition for the problem at hand. Thus, this work extends the recent series of
existence results for singular one-phase Stefan problems in one space dimension
that can be found in [DIRT15a], [NS19a], [HLS18], [CRS20]. As therein, our
existence result is obtained via a large system limit of a finite particle
system approximation in the Skorokhod M1 topology. But, unlike for the
previously studied one-phase case, the free boundary herein is not monotone, so
that the large system limit is obtained by a novel argument.
