I guess that you are dealing with 12.7mm (0.5"
or 15.2mm (0.6"
strand in multistrand configuration. Since it is a box girder the subject tendon may be in the web or the flange.
You seem to imply that only ONE cable slipped, but the live end anchorage did displace - seems a bit strange. When you say "cable" you may mean tendon, consisting of multiple strands within a group. I usually refer "cable" to mean an individual strand, but this nomenclature does vary around the world. Sometimes the wedges can slip and a single strand may release, but this is an individual strand grip problem not an anchorage problem.
BUT, in your case i think you mean all strands (the complete tendon/cable) "slipped" as evidenced by the anchorage displacing and probably the concrete crushed/burst immediately around the anchorage. Either the anchorage reinforcemnt was omitted and/or the concrete was not sufficiently compacted behind the anchorage.
Indeed, it would seem that a repair is required. The tendon need to be first destressed using a open-ended destressing chair, and the hydraulic jack (preset the jack at close to full stroke of the jack) needs to deload the wedges, then remove the wedges, and then deload the anchorage via the hydraulic jack. Upon completion of this the concrete can be repaired and after suitable duration/cure, restressed.
You need to ask you P-T subcontractor for the methods that they will engage to do this specialized work.
If you have more information on the tendon configuration and actual nature of the cable slip/anchorage rupture, i may be able to assist further.
HTH
