Late first decade, 21st century
Romanians and Bulgarians are "not allowed to work."
But, as members (since January 2007) of the European Union, they are allowed to have a PPS number. (The PPS is analogous to the American "Social Security Number," or the Dutch "Sofinummer." It is a string of integers (and one letter) that is an individual's universal identifying code in his or her interactions with governmental offices.)
If one is clever, lucky, and/or persistent, getting a PPS number is easy for the Romanian or Bulgarian resident of Ireland (and is in fact an entitlement, although the answer depends upon one's reason for asking or [as for example in Kilkenny] whether or not "the old lady" is attending the reception desk.)
Even with a PPS number, the Romanian or Bulgarian is still not necessarily legally entitled to work. But with it, he or she can get a job, and pay taxes, as long as an employer is unaware or unconcerned about that legal technicality.
The employer can in fact pretend to have been unaware the employee had a PPS number, after all. At the same time, and especially with any language difficulties involved, the employer can still treat the employee as a second-class worker, an illegal worker exploitable, in the ancient mathematics of black-market labo(u)r.
It is a simple matter to exploit the duality of the legal status of Romanians and Bulgarians in Ireland (which followed on the lead of England in restricting their entitlement to work.)
It would be an unusual employer who could entirely avoid taking advantage of such an opportunity.