  In this paper we investigate BSDEs where the driver contains a distributional
term (in the sense of generalised functions) and derive general Feynman-Kac
formulae related to these BSDEs. We introduce an integral operator to give
sense to the equation and then we show the existence of a strong solution
employing results on a related PDE.Due to the irregularity of the driver, the
$Y$-component of a couple $(Y,Z)$ solving the BSDE is not necessarily a
semimartingale but a weak Dirichlet process.
