Sure it can.
@MAdcox in an earlier post provided proof of this. Put even a relatively small hole in the heart/lungs of an animal, and it will die. While the end was successful in that the intended animal was killed, I would still say such performance is bullet failure as the bullet did not perform as expected. Examples like that go to show that bullet placement is still very important and arguably more so than the bullet itself.
But then as the wise sage
@Velo Dog has said, a well placed frozen herring could kill an animal too, but what's the point?
The question for me when it comes to choosing a bullet is not if the bullet can fail? Bullets get put through a ridiculous test when you think about it. And I'm quite certain all bullets can fail to perform as expected. The question is not IF it can, but HOW OFTEN do they? The pic of the Barnes that failed to open earlier isn't the first I've seen. I've seen quite a few just like it. But weighed against how many hunters have used them successfully , my gut feel as I cannot possibly attain accurate statistics is that it's relatively low.
Furthermore unlike some other bullets, the manner in which they fail to perform is in opening. I can accept that failure far more easily than a bullet that shatters on impact and fails to penetrate.