That crossways thing through the stock is a recoil lug. The lug on the receiver bears against it to spread out the recoil and keep from battering the wood stock.
A stock recoil lug is usually used only on rifles that will undergo a lot of firing (like military rifles), or that have heavy recoil (like big bore sporters). Most sporter stock don't have them because they won't be fired enough or don't have enough recoil to crack the stock.
You can put one in your new stock if you want, but note that it has to be carefully fitted with the receiver; if there is a gap that allows a recoiling receiver to get a "running start", a cracked stock will become more, not less, likely.