Was there a backstory or karmic reason for the tiger's appearance and death before Sai Baba?

Yes, Chapter 31 speculates on a karmic backstory for the tiger. The text suggests that the tiger may have been a meritorious person in a past life who, out of pride, insulted a devotee of Hari. As a result, the devotee's curse caused him to take on the "cruel birth" of a tiger. However, a counter-curse also seems to have been in effect, which ultimately led the creature to Sai Baba's feet. Through Sai's darshan, the sins were burned away, the bonds of past karma were broken, and the being was freed from the "cruel body's bondage," thus achieving salvation.