An almost routine part of an open approach to the nose is reattachment of the upper lateral cartilages to the nasal septum after trimming them, placing dorsal spreader grafts or both. The septum and the upper lateral cartilages develop embryologically as one cartilage and should be repaired. They are sutured in place. If you had a disruption from trauma, they can also be sewn back in place. Failure to re-establish the structure of the upper laterals to the septum can contribute to what is called a inverted V deformity as scar tissue pulls the unattached upper laterals down and out.
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.