Tenancy check what is needed to be accepted

Dear fellow landlords,

We all have experienced that bad tenant got new place even without referencing from us when they leave our place. Some tenant had CCJ or bad credit, it didn’t show up on the check. What is the point of having the check?

So the questions is what kind of checking the agency/next landlord do? Or as a landlord, if you do the check yourself, what kind of the things are you looking for? At the moment, I do check myself on their employment and contact current landlord for referencing. Could you share your experience on this? Thanks.