We provide a unified approach to a priori estimates for supersolutions of BSDEs in general filtrations, which may not be quasi left-continuous. Unlike the previous related approaches in simpler settings, our results do not only rely on a simple application of Itô's formula and classical estimates, but use crucially appropriate generalizations of deep estimates for supermartingales obtained by Meyer. As an example of application, we prove that reflected BSDEs are well-posed in a general framework which has not been covered so far in the existing literature.