Ok, I'm no lawyer, but I am pretty confident in my understanding. If I am wrong, someone please correct me.

When you sign the I-864 Affidavit of support, you are entering into a binding contract with the US government that basically says "I accept liablity for any burden this person may cause on the people of the United States." So, what happens, is if this person goes on welfare or something at some time in the future, the feds send you the bill. To prevent shams, her first green card is only good for 2 years. After that she gets regular permanent residency, and even if she dumps you, you dump her, etc... she is under no obligation to leave. However, the government says it was your idea to bring her here in the first place, so you are still responsible. If she becomes a citizen or abandons her residency, you get out of your oblication. thats the only way.