From this answer, Brabrika had an arrow that could find the vulnerable spot(s) of a person and was able to find Krishna's vulnerable spot that was His feet's sole.

The ash fell on the hair of Bhisma; on the neck of Karna and Drona; on the thigh of Duryodhana; on the chest of Salya; the brilliant ash fell on the necks of Sakuni and Bhagadatta; on the sole of the foot of Krsna; on the necks of Drupada and Matsya; on the hip of Sikhandin; on the neck of the commander-in-chief of the army (Dhrstadyumna). The red ash fell on the vulnerable spot of everyone. But the ash did not touch the Pandavas, Krpa and Asvatthama.

And this website gives a story for it. It says sage Durvasa cursed Krishna for not applying a sweet dish on His leg

  1. Durvasa did not spare Lord also from his curse. One day, Durvasa was eating kheer (a sweet dish made of rice and milk) in persence of Lord. Durvasa ordered Lord to apply the left over kheer on his body. He applied it on the full body but did not apply on his feet thinking of the kheer to be consecrated. Durvasa got angry at this and curses Krishna that since you did not obey my orders and did not apply the kheer on your legs, your legs will not remain impenetrable and unbroken. It is the famous story that he left this world because an arrow by a hunter hurt his toe. So my questions are:
  1. Where is this (Durvasa's curse) story mentioned?

If this story is not authentic then,

  1. Why/how was Krishna's feet became vulnerable?