Another theory is that this is the sword that will later belong to the Witch-King of Angmar, the leader of the Ringwraiths, with which he stabs Frodo on Weathertop in The Fellowship of the Ring.

she is literally the only being to ever have lived that successfully killed a Ringwraith. That alone speaks to her ability ...

The sword that graced the hand of the White Lady ... The Nazgûl, Sauron's Ringwraiths, were led by the sadistic Witch-King, ...

The sword could be found throughout the LOTR and Hobbit series, with Elrond using it against Ringwraiths in The Battle Of The Five Armies and slaying Orcs with it during the War of the Last Alliance.