During repair of indirect inguinal hernia, while releasing the constriction at the deep inguinal ring, the surgeon takes care not to damage one of the following structures -
The deep inguinal ring lies immediately lateral to the inferior epigastric artery so quite obviously the artery is being in danger of getting damaged while releasing the constriction at the deep inguinal ring.
Falx inguinalis (conjoint tendon)
Interfoveolar ligament
Inferior epigastric artery
Spermatic cord