Deformation conjecture for semi-log canonical foliation singularities

Let $f\colon (X, \mathcal F) \rightarrow T$ be a flat family of integrable distributions such that $K_{\mathcal F}$ is $\mathbb Q$-Cartier and the fibres of $f$ are deminormal. Suppose that $\mathcal F_t$ is semi-log canonical for some closed point $t \in T$. Then there exists a Zariski open subset $t \in U \subset T$ such that for all $s \in U$, $\mathcal F_{s}$ is semi-log canonical.

Semi-log canonical singularities deform. Under these hypotheses, semi-log canonical singularities of the fibre at $t$ persist for all fibres over some Zariski-open neighbourhood $U$ of $t$.

This conjecture concerns the openness of semi-log canonical singularities in families of foliations and is presented as a central problem in constructing moduli spaces. The analogous assertion for canonical singularities is false, but the semi-log canonical version is left open.