  The mechanical behavior of two-dimensional (2D) materials across 2D phase
changes is unknown, and the finite temperature ($T$) elasticity of paradigmatic
SnSe monolayers -- ferroelectric 2D materials turning paraelectric as their
unit cell (u.c.) turns from a rectangle onto a square -- is described here in a
progressive manner. To begin with, their zero$-T$ {\em elastic energy
landscape} gives way to (Boltzmann-like) averages from which the elastic
behavior is determined. These estimates are complemented with results from the
strain-fluctuation method, which employs the energy landscape or {\em ab
initio} molecular dynamics (MD) data. Both approaches capture the coalescence
of elastic moduli $\langle C_{11}(T)\rangle=\langle C_{22}(T)\rangle$ due to
the structural transformation. The broad evolution and sudden changes of
elastic parameters $\langle C_{11}(T)\rangle$, $\langle C_{22}(T)\rangle$, and
$\langle C_{12}(T)\rangle$ of these atomically-thin phase-change membranes
establishes a heretofore overlooked connection among 2D materials and soft
matter.
