Rejected-proposal distribution ($r(z)=\frac{Mg(z)-f(z)}{M-1}$)

With normalized densities $f,g$ and envelope $f\le Mg$, $M>1$, conditioning a proposal on rejection gives density $r=(Mg-f)/(M-1)$. It can be used as an importance sampling proposal only if it covers the relevant target support. If $Mg=f$ on a set of positive target mass, rejected draws never visit that set.