It is revealed in Layer 08 that Alice is attracted to a teacher in her school. Evil Lain spreads this information through the Wired, and although Alice wants to believe Lain did not do it, evil Lain appears in her room and laughs at her. Lain eventually deletes everyone's memories of these rumours - except for Alice's.
In Layer 12, Lain says that Alice is special because she became Lain's friend before she connected with everyone through the Wired. Alice teaches Lain that there is still value in having a physical form, placing Lain's hand over her heart to feel her heartbeat.
By the conclusion of the anime, a grown-up Alice is married -- possibly to the same teacher that she had been in love with in Layer 08.