I don't think much was ever done to elaborate on him. He was a joke character that didn't really last past UMK3/MKT. I know they created some story for him but even that was pretty shallow.

RAIN

Origin: Edenia
Species: Human
Affiliation: Worked for Shao Kahn
Allies (?): Kitana
Enemies (?): Shao Kahn

Mortal Kombat Trilogy: Rain was the son of an Edenian general who was
killed during Kahn's invasion 10,000 years before. During then, Rain was
a baby who was hidden away. He made his return before Kahn's Earthrealm
invasion and joined the emperor out of fear. It's hard to say what
happened next for the purple ninja. Either he fought for Kahn until dying
or escaping or Kitana had informed him of his past, allowing him to join
the good side.

Deception: Whereabouts unknown.

Miscellaneous Facts and Notes:

Rain was shown in the intro for UMK3 in the arcades, but he was not
actually in the game. It was just those wacky Midway guys trying to trick
you into inserting more tokens.

Before his story was finalized, the idea for Rain was that he was going to
be a member of the Lin Kuei. This made it in to some of the manuals by
accident.

He exists as a reference to Prince. Get it? Purple? Rain?

Taken from the MK plot FAQ. Hope it helps