The anime has finally reached the famous part of Big Mom’s flashback, in which the young Linlin is heavily implied to have devoured Mother Carmel and the children alive and, by doing so, she obtained Mother Caramel’s Soru Soru no Mi devil fruit powers.
So the logical conclusion is that because Big Mom ate Mother Caramel, she got her powers. Essentially, Cannibalism gave her Mother Caramel’s Soru Soru no Mi Devil Fruit.
But does this apply to everyone in the One Piece world? No
I think that this phenomena is particularly exclusive to the Soul-Soul Fruit(Soru Soru no Mi). Think about it, the fruit lets you control souls and when Linlin ate Mother Caramel, her soul transferred to Linlin and so did the powers. It just happens to be a property of the Soul-Soul Fruit and by a major coincidence Linlin was able to trigger it.
So what does this mean for Blackbeard?
Another person who was able to take a devil fruit power from someone else is Blackbeard, who took the Gura Gura no Mi from Whitebeard. Blackbeard definitely did not eat Whitebeard. So there’s another way (other than the Soru Soru no Mi) to take someone’s devil fruit power. And once again, it has to do with the devil fruit, but this time it’s Blackbeard’s Yami Yami no Mi.
Blackbeard specifically researched the Yami Yami no Mi and searched for his whole life for it. Taking other people’s fruits, while under a blanket in complete darkness, must be part of its ability.
*Theory by sir_tejj