A token that’s copying Blitz Hellion will be shuffled into its owner’s library when this ability resolves, then will cease to exist. For practical purposes, the token should not actually be put into the library, though the library is still shuffled.

Blitz Hellion’s last ability triggers at the end of each turn in which it’s on the battlefield. If it’s not on the battlefield by the time this ability resolves, nothing happens. Blitz Hellion stays wherever it is, and its owner doesn’t shuffle their library.