The Dominican Priory of the Holy Cross has left no standing remains above ground, yet excavations carried out between 1997 and 2000 kept turning up articulated skeletons, limestone walls nearly a metre thick, and tomb structures, all sealed under layers of cobbles, demolition rubble, and modern fill. Of eighteen trenches opened across the Abbey carpark in 2000 alone, twelve contained intact medieval walling and eight contained burials. The priory is, in every meaningful sense, still there.

The house was founded in 1243 by John Fitz Thomas FitzGerald, and he was among its first notable burials, interred there in 1261 alongside his son Maurice following their deaths at the Battle of Callan. The friary quickly became the dynastic burial ground of the FitzGerald lords and earls of Desmond, a family who dominated much of Munster politics for the following three centuries. Contemporary records confirm the burials of Maurice, 1st Earl of Desmond, who died in 1356, Thomas, the 8th Earl, who died in 1468, and Joan, daughter of the 3rd Earl, who died in 1411. One nineteenth-century scholar counted three lords and seven earls of Desmond said to have been laid to rest within its walls. The priory had a violent history even while functioning: in 1295 a man named Nicholas Strange was charged with stealing silver and wheat from its chapel of St Mary, and in 1325 Diarmait Mac Carthaig, king of Desmumu, was killed inside the priory itself, reportedly by Nicholas FitzMaurice or his son William. By 1580, during the Desmond Rebellions, the Lord Justice Sir William Pelham garrisoned the building with 300 footmen and a company of horse, noting it was the only suitable structure the retreating earl had not destroyed. A survey carried out in 1584 described it as ruinous and in great decay, though it recorded that it had been large and ample before the rebellion, with a church in which the ancestors of the earl were honourably buried. The priory was granted to Edward Denny in 1587.

The 1997 testing by Martin E. Byrne was constrained in an almost absurd way: the low roof levels and door lintels of lock-up units on the site prevented a mechanical digger from entering, so the machine was parked outside and its arm extended through the doorways to excavate. Even so, skeletal remains were found nearly two metres below the present surface, and a substantial wall was uncovered in a second trench. The following year, Laurence Dunne's work on Lower Abbey Street exposed further limestone walling set in clay without mortar, interpreted as the basal remnants of the south-east range of the abbey. The bones of earls and the stones of their church survive, compressed and layered, in the ground beneath ordinary urban life.