Any person who entered the United States illegal is bared from filing an application for an adjustment of status under the Immigration and Nationality Act, INA. People who entered the United States illegal are sometimes referred to in immigration terminology as EWI or EWIS, i.e. people who Entered the United States WithoutInspection.
Generally speaking the INA bar EWIs from adjusting status in the United States. There are some exceptions to this rule such as section 245(i) of the INA, filing under the Violence Against Women Act – VAWA, filing applications with the Immigration Court for Cancellation of Removal, Asylum, etc.