Effective March 4th, 2013, a new regulation published by the Obama administration, similar with the recent DACA last year, is changing the application process of an old waiver. This, again, is not a law since it was not passed by the Congress. It is not an amnesty either.
The same individuals that qualified for the "old" waiver, qualify for the new process. That is to say that only certain relatives of U.S. Citizens can apply for it. Also, the waiver still refer to "extreme hardship"suffered by the U.S. Citizen relative, not by the beneficiary. What is changing is just the processing of the waiver while the beneficiary is still in United States and is aiming to considerably shorten the time the beneficiary will have to spend separated from their U.S. Citizen relatives.
A person who enters illegally in United States (without any visa and without inspection) will not be able to obtain, under the current immigration laws, permanent residency, while in U.S., even if they are married with a U.S. Citizen or if they have U.S. Citizens children over 21 years of age. They will have to, first, leave U.S. and, their relatives to petition for them, while they would stay abroad until they receive the documents. This process might take a really long time. If the person has been illegally present in United States for less then a year, the moment they leave United States, they are barred to apply for any kind of visa for 3 years. If they have been illegally present for over a year, they are barred for 10 years.
If a person is barred for 10 years, there is this waiver in place to ask for the forgiveness of the 10 years bar, but it requires to show "extreme hardship" suffered by the U.S. Citizen relative. Thus, the waiver cannot be used in all cases, and by anyone. The new regulation is trying to alleviate somehow the need for these exceptional cases to have the waiver processed in U.S. and have the beneficiary spend as little time as possible abroad, apart from their U.S. relatives who would otherwise be subjected to "extreme hardship".