The problem is as much the short grain in the stock at that point. In other words, the grain angle is diagonal across the stock rather than parallel with the stock. Short grain is fragile by comparison to long grain (parallel to the stock). There could also be a crack in the wood from the mfg or milling process. May be tough to fix that, but reinforcing the stock with dowel stock is not a bad idea.
Inletting and relieving the stock involves removing stock so that the recoil forces are resisted by a solid facing on the stock, in a direction parallel to the stock. I'm not sure that's possible when the grain is running off like it is at the stock's wrist.
I'd give the reinforcing a try, but be prepared to replace the stock. If it were Ruger or other reputable mfg, you might get some relief from them, but it's a Stoeger. Que Sera Sera.