Left to its own devices, it is just a loose modifier and not a sentence.
Absolute constructions don't have a finite verb. Instead, they must have a participle, past or present
Give such a construction a sentence to modify, and it will attach itself to it and work with it just fine:
The troubles he's been through
gone away, he is back himself, alive and kicking.
The troubles he's been through
showing on his haggard face, he is now a listless apathetic creature, ready to retire.