Can immigrants who left or were deported get Obama Amnesty?

Generally speaking, amnesties require you to meet the continuous presence eligibility requirement and so is the case for RPI visa legal status, but in case of the Border Security, Economic Opportunity, and Immigration Modernization Act of 2013, there is one exception on humanitarian grounds so that families are not separated.  What it means is that if an immigrant was deported for non-criminal reasons (like driving without a license or working without authorization) he or she can apply to re-enter the United States in RPI status if they are the spouse of or parent of a child who is United States citizen or lawful permanent resident or a DREAMer.  The process, obviously, will work a little different for those aliens who are outside the USA, because they will not be able to enter the country before they are approved.  This provision cannot be used to bring family members who were never in the USA nor can it be used if they were not married at the time of deportation (meaning that you cannot marry after they were deported).