Shion ~Memories of the Past~

 is Disc 1, Track 24 on the Xenosaga Original Soundtrack and Disc 1, Track 1 on the album. ('Shion ~Memories of the Past~' is an unofficial translation, as seen in the VGMdb listing of the album.) It, alongside Game Over and Shion ~Emotion~, is one of the tracks based on the melody at the start of.

It plays on the Game Over screen (after all active playable characters have their reduced to 0 in battle).