Feedthough/via that straddles (i.e., is bisected by) the cut edge of a PCB?

I can't see any way to do this, reliably.  So, imagine a house won't
let it through DRCs, regardless of diameter or weight of foil, etc.
Or, is there another (not exhorbitantly pricey) technology for precisely
cutting boards that would keep the structure (at least the part that is
not lost to the cut) mechanically (and thus electrically) intact?
Else, I will use another -- more expectantly reliable -- approach