The Xindi-Avian species was an extinct member of the Xindi race, wiped out during the conflict between the six Xindi species which destroyed their homeworld, sometime in the 2030s. As far as known, none of them fled before their homeworld was destroyed.
Gralik Durr's grandfather, who had resided on Xindus, remembered a time before the planet's destruction when Avians would flock overhead, filling the sky. (ENT: "The Shipment")
A skull of an Avian was kept at the Council's location. CommanderDolim commented that the Council chamber had "the stench of the Avians' failure to survive". (ENT: "The Council")
The Xindi-Avians were originally devised as a sixth member of the Xindi Council, though this idea was discarded due to uncertainties concerning how to actualize them as physical designs. Executive Producer Brannon Braga explained, "We did [consider avians, or bird people, among the original five], but we thought two CGIs [the Xindi-Aquatics and Insectoids] were enough–and you don't want to do actors as bird people." (Star Trek: Communicator issue 149, p. 50)
The prop used for a Xindi-Avian skull in "The Council" is a model replica of a giraffe skull.