What happens to upper lateral cartilage of the nose when its disconnected?

The upper lateral cartilage is the cartilage in the mid portion of the nose, it can be disconnected in trauma or during rhinoplasty maneuvers.  It can be reconnected, and should be in most circumstances or it can result in breathing difficulty and cosmetic deformities such as inverted v deformity and nasal deviations.  The upper lateral cartilage can be reattached to the septum with suture and spreader grafts are usually used to support them into a position which is best cosmetically and to open the airway.  Hope this helps.

 The upper lateral cartilage can be disconnected from the nasal bones from a traumatic injury or from surgery. From trauma it usually results in a concave or" C" shaped deformity of the nose whereby one upper lateral cartilage is concave and the other one is convex. When both upper lateral cartilages fall inwards after a rhinoplasty, it is called inverted V. deformity. To prevent this, spreader grafts composed the patient's own cartilage are inserted at the angle between the septum and upper lateral cartilage connection to bolster the upper lateral cartilage and push it outwards. This is done for both cosmetic and functional breathing reasons.

If I understand your question, the upper lateral cartilage, which gives the side of the nose support can be injured, bent, crushed or damaged.  The ULC does attach to the nasal bone above and  to the tip cartilages below and to the septum in the midline.  It is possible that the ULC could be "disconnected" from its attachments in surgery.  It is usually easier to "graft" or support the side of the nose with another piece of cartilage than trying to "reconnect" the damaged piece.