The first chapter ends with a death—the death of our main character in fact. She dies quite a few times over the course of the book, and this line, or some variation thereof, describes each one of her deaths as a fading into darkness before being reborn. There's no white light, like some people say they see.
"She's gone. Dead before she had a chance to live." (2.12)
The death of Ursula at birth is tragic, but the irony here is that she has had the chance to live. At this point, we're not sure just how many times, but her life is ever-repeating, which takes some of the edge off her death.
[Hugh] laughed and said, "What's going on here, then?" picking up Ursula and tossing her casually in the air, only stopping when she started to choke on a sugar lump. (6.48)
In any other book, this line wouldn't really mean anything. But in Life After Life, we've already seen Ursula die twice. She narrowly avoids death by sugar cube here.
Pamela said [Sylvie's suicide] was the coward's way out, but Ursula wasn't so sure. She thought it showed a rather admirable clarity of purpose. (18.10)
This line shows Ursula's feelings toward death (i.e., it's inevitable) and foreshadows her eventual suicide in one of the timelines, an action she commits with clear purpose.
To Ursula Todd, for good work. It would do for an epitaph too, she supposed. (18.28)
Ursula thinks a lot about death in this chapter (one of the chapters in which she later dies). This epitaph idea perfectly sums up how Ursula wants to be remembered: for good work.
"Well, we all get on," Sylvie said, "one way or another. And in the end we all arrive at the same place. I hardly see that it matters how we get there." (21.16)
Sylvie has a very laissez-faire approach to life—she's all, who cares? We're going to die anyway. That seems awfully defeatist to us (and if she truly believes this, why is she so snooty to Ursula about her life decisions, hmm?).
[Ursula] had never chosen death over life before and as she was leaving she knew something had cracked and broken and the order of things had changed. Then the dark obliterated all thoughts. (24.241)
This is a major breaking point for Ursula—she kills herself and her daughter, but she does it because she thinks it's for the best. It's important to remember that she is choosing death here, not rebirth. Despite living over and over again and having feelings of déjà vu, it doesn't seem like Ursula ever truly realizes that she is born again and again.
Ursula wasn't convinced that the dead went anywhere, except into a void, black and infinite. (25.34)
This quote backs up what we thought about the last one: that Ursula believes she dies, not that she is reborn. While there may not be an afterlife for Ursula, there's no oblivion either.
"We never know when it will be the last time," [Ursula] said to Izzie. (25.256)
This is a typical sentiment when it comes to death, but it's ironic coming from Ursula's mouth. Going forward, she will know when it's the last time, thanks to her memories of past lives.
"He was my boy," Sylvie said vehemently, "don't you dare say he was yours," although she knew, guiltily, that she mourned less for Roland than she would have done for one of her own. (26.54)
Sylvie uses Roland's death as a way to feel superior to Izzie, as though coping with death is like some sort of grief Olympics.