Throwing the money at Liza is one way the Underground man seeks to establish some type of power in an existence that lacks it.  After spinning tales of how superior he is to her and how her life will be condemned to misery if she does not leave prostitution, the Underground Man has made himself to be a hero, if only for a moment.  Yet, when Liza arrives at his home, it is apparent that she understands his weaknesses and how he is incapable of love.  After seeing his home and seeing who he really is, she understands him.  She recognizes that although he needs love and needs some type of redemption badly, she also recognizes that he has become a product of the world around him.  He cannot be saved for this reason.  Someone would have to literally sacrifice themselves to do so and even this is no guarantee.  The same degrading that he spoke to her would happen if she remained in prostitution is the same that would happen to anyone if they fell in love with the Underground man.  At this moment, when she fully understands how he is condemned to being a product of his own environment, she transcends her with her embrace.  This jarring and powerful breaking of environmental context and contingency is seismic for the narrator.  His only way to reestablish some level of power and some level of normalcy is to bring back the environment that he hates so much and throw the money at her.  Yet, in the end, she has become the figure that proves to us that there can be saving if individuals understand the need and demand to not become a part of the world that surrounds and corrupts them.  She has understood this, while seeing through the narrator in the process.