Non-EEA nationals who wish to reside in the State may only do so on the basis of a valid application for immigration permission under one of the immigration streams operated by my Department (work, study, family reunion etc). Whether previous legal residence in the State will have a bearing on that application will depend on the nature of the individual case.
In the absence of more substantive information and in order to come to a definitive position, I would suggest the Deputy forwards the details of the particular case via the INIS Oireachtas mail facility.