Locked it away for no-one to see? The cross was distributed to so many churches that Erasmus (very slanderously) said that there were so many relics that they must’ve used the entire forests of Lebanon. (In truth, they total only about 100 kg; it takes 100,000 grams to make 100 kg!)
People just tend to ignore such relics; the Sacred Chalice (Holy Grail) has been in Spain since the third century; it’s currently in the Cathedral of Valencia, where it was restored by a bunch of Frenchmen at the time when a boy named Arthur was Duke of Brittany while John I usurped the British throne.
The crown of thorns lies in Cathedral of Notre Dame; the sacred burial cloth lies in Turin; over the tomb of Jesus, a great Church is shared (unfriendlily) by Orthodox and Catholic priests.
I saw a nail from the Cross in a museum in Vienna.
I have seen the HOLY GRAIL AND THE CROWN OF THORNS! PRAY6TO SEE THE SHROUD!