It's conflating books and show, but there's some discussion about Starks, White Walkers, wights, first men, and the crypts of winterfell.
More or less, that's why most every sarcophagus is adorned by that Stark's sword, the iron binds the would be wraith from rising again. Now, if the folks in the crypt take the swords off the graves, or Lyanna Stark is actually buried instead of just memorialized (Brandon the Shipwright), there may be a grave or two that rise from the dead.
There's a lot of unexplored back story to the Starks and their affinity for being skin changers or wargs, and why the Boltons and Carstarks had been at odds with them for so long. Odds being an understatement of historical notation when the families would hunt and kill one another for #reasons.
The Starks come from stock of the First Men, thus why many in the North still pray to the old gods and the weirwood trees. The other inhabitants of Westeros are more akin to the Andals. Thus, the Starks have powers that the other folks don't because of old religion and association/exposure to the Children of the Forest, etc. etc. Does any of that make sense, of course not. I'm not definitive and the material is a bit convoluted. But yeah, the dead rising in the graves is something I totally expect to happen, but in story there is a solution for it already. I will #faceturn on the show if they give a nod to this and portray this detail accurately.