You would then be given temporary guest worker status pending a criminal background check that you would pay for. You must sign a statement indicating that you will not apply for or receive any government assistance and that any felony or crime which can be charged as a felony will be immediate grounds for deportation. After you clear everything then you would be given a more permanent immigration status, something less than "permanent resident" and you would never be eligible for Citizenship.
If it is found that you have committed a felony while in the US, you will be deported using the application fee as your plane or bus fare to the border.
There are those who would call this "Amnesty".
I see no reason for the original illegal family members not to pay a stiff price. However, there is no way to make an anchor baby pay. Also, those minor children brought by their parents are not nearly as culpable as the parents.