My mother was retained when she first entered the USA, 18 years ago. She was detained while being in a terrible medical condition, so she was given a case to stay here. However, she lost due to a fraud-- fake lawyer. She was given some months to leave the country legally, but she decided to stay instead. Thus, she has a deportation record in the system. Will she be eligible for DAPA?
As long as your mother has been physically present in the U.S. continuously since January 1, 2010, the old case should not affect her eligibility for DAPA. There may be other factors that impact her DAPA eligibility, however (for instance, certain criminal convictions or travel outside of the U.S. since January 1, 2010), so it is a good idea for her to have a consultation with a reliable attorney or legal services organization to assess her eligibility for DAPA or any other relief. Here is a list of low-cost service providers (though they are usually not free) http://www.justice.gov/eoir/probono/states.htm