Alice Greenwood is Dana's long-dead ancestor, but Dana gets a chance to meet her when she travels back in time. Alice starts life as a free woman, but gets thrown into slavery after she tries to run away with a fugitive slave named Isaac. Alice is disgusted by Rufus Weylin's attempts to have sex with her, but finally gives in after Dana talks her into it. As the book says, "She went to him. She adjusted, became a quieter more subdued person. She didn't kill, but she seemed to die a little" (4.12.1). It's clear that giving into Rufus has killed something inside Alice. The submission is especially bad when you consider that she began her life free and only lost her freedom as a result of Rufus trying to rape her.
It's understandable that Alice becomes resentful to Dana, especially considering that she knows Dana has some sort of close bond with Rufus. She has no one else to take out her pain on, so she uses every chance she can to call Dana a traitor to her race. For example, she says at one point, "You don't want to hear me, get out of here. The way you always suckin' up to that woman is enough to make a body sick" (5.7.26). In the end, Alice kills herself because she thinks that Rufus has sold her children to a white slave trader. Little does she know that Rufus has made up a lie just to put her in line. Her suicide is a tragic end to a tragic life, and it's the last straw before Dana grabs a knife and kills Rufus.