I don't know of any algorithm to cull non-winnable Klondike games. Playing deal-1 instead of deal-3, and with unlimited flipping of the stock, the win chance is probably close to 50%, but that still makes 2000 in a row statistically impossible.
My guess is that the poster's mom was actually playing FreeCell, in which nearly every game is winnable and people do get streaks like that.
You don't need an algorithm. You can just record seeds that are solvable. The current version of Klondike in MS Solitaire is winnable unless you play "Random" difficulty.
It’s quite doable, if you don’t mind culling some winnable games too. The object isn’t to have a perfect classifier.