  This paper is devoted to deformations of Lagrangian submanifolds contained in
the singular locus of a log-symplectic manifold. We prove a normal form result
for the log-symplectic structure around such a Lagrangian, which we use to
extract algebraic and geometric information about the Lagrangian deformations.
We show that the deformation problem is governed by a DGLA, we discuss whether
the Lagrangian admits deformations not contained in the singular locus, and we
give precise criteria for unobstructedness of first order deformations. We also
address equivalences of deformations, showing that the gauge equivalence
relation of the DGLA corresponds with the geometric notion of equivalence by
Hamiltonian isotopies. We discuss the corresponding moduli space, and we prove
a rigidity statement for the more flexible equivalence relation by Poisson
isotopies.
