  We consider a mean field game (MFG) of optimal portfolio liquidation under
asymmetric information. We prove that the solution to the MFG can be
characterized in terms of a FBSDE with possibly singular terminal condition on
the backward component or, equivalently, in terms of a FBSDE with finite
terminal value, yet singular driver. Extending the method of continuation to
linear-quadratic FBSDE with singular driver we prove that the MFG has a unique
solution. Our existence and uniqueness result allows to prove that the MFG with
possibly singular terminal condition can be approximated by a sequence of MFGs
with finite terminal values.
