Here's what a Biblical literalist says on that very verse (from a debate I'm having on /r/debatereligion):

I would encourage you to consider these injunctions within the context of the ancient Near East cultures. What man would marry a woman who was not a virgin? If he had a choice, no man. Thus, a woman who had been raped, being "damaged goods," is fated to wander the streets homeless when her parents die (if they don't kick her out right away).

The Jewish law here allows for protection of the victim of the rape. If the man is going to follow the law to marry the woman he has just raped, then he will also hold himself accountable (or be held accountable) to take care of her as well. Thus, the woman is not homeless; she is taken care of by her rapist. I don't know how these relationships played themselves out, if there may have been some reconciliation at some point, or if they were cold, distant marriages (honestly, the culture- and time-specific differences between us and them would make this hard to discern anyway), I don't know. But I imagine that was the purpose of the law.