What happens when you die in the Digital World? Alice happens.
We know only a couple, concrete facts about Alice: she's Dolphin's granddaughter, and she was sent with Dobermon on a mission by the Digimon Sovereign.
The remaining details about her character, according to series head writer, Chiaki J. Konaka, are...ambiguous, to say the least:
"The following is my own personal thoughts, not necessarily canonical or correct, but...
There is a scene in which Dolphin looks at a framed picture of his granddaughter, and calls out her name...
In the framed picture, Alice shows an innocent, child-like smile.
But Dolphin (played by Mr. Masami Kikuchi in the Japanese) called out to Alice with great feeling in his voice.
As I listened to the recorded dialogue, I got a strange feeling... that perhaps, long before the story of Digimon Tamers had started, Alice had left this world.
Mind you, this is just my own imagination."
Various theories cropped up, but I'm firmly in the "Alice is dead and what we saw of her was a ghost" camp. Between the scenes with Dolphin and the final shot we see of Alice disappearing as she wanders off, it's a safe bet to make.
So, how did Alice die, and what made her death so unique she could return as a ghost? Furthermore, what's her relation to Dobermon?
Going by Konaka's own suggestion that Alice had left this world "long before Digimon Tamers started," I believe Alice stumbled into the Digital World on accident, some time after the Wild Bunch had shut down its project. Because the project had long since shut down and no one had witnessed Alice's abrupt disappearance, her family suspected her case to be that of a missing person's or a kidnapping. Dolphin, having been the one to have looked after Alice before her disappearance, shouldered much of the blame, and aided Alice's parents in their endless pursuit of their daughter's whereabouts.
Meanwhile, Alice was trapped in the Digital World, but not without aid in the form of her partner, Dobermon. The rest of the details, such as how long she was in the Digital World before her death, or just how earlier she visited before Tamers, I'm unsure of, but here's the meat of the deal, and it's based on what Dobermon said in the dub:
It's dub-only, but I'm rolling with it regardless. If a human dies in the Digital World, because their data is unique from its native inhabitants, it spreads out into an entirely different form of data--one that goes either scattered or transferred to the partner Digimon. The results of this are also dependent on the circumstances of the death--in Alice's case, her death was the result of a sacrifice on her part, either by means of protecting Dobermon or multiple Digimon (as Dobermon hints that her help was something grand in scale). As such, her data granted Dobermon the ability to travel freely to the Real World, and allow a physical manifestation of Alice's "ghost" to appear.
Alice died a noble, heroic death, that would eventually aid Dobermon and the Tamers' victory over the D-Reaper. The real tragedy is that none of her family or friends would ever learn of what happened to her.
To end with a quote by Konaka, "Mind you, this is just my own imagination."