  We study the optimal stopping problem of McKean-Vlasov diffusions when the
criterion is a function of the law of the stopped process. A remarkable new
feature in this setting is that the stopping time also impacts the dynamics of
the stopped process through the dependence of the coefficients on the law. The
mean field stopping problem is introduced in weak formulation in terms of the
joint marginal law of the stopped underlying process and the survival process.
This specification satisfies a dynamic programming principle. The corresponding
dynamic programming equation is an obstacle problem on the Wasserstein space,
and is obtained by means of a general It\^o formula for flows of marginal laws
of c\`adl\`ag semimartingales. Our verification result characterizes the nature
of optimal stopping policies, highlighting the crucial need to randomized
stopping. The effectiveness of our dynamic programming equation is illustrated
by various examples including the mean-variance and expected shortfall
criteria.
