He was caught up to by her.†
He had been ahead of her but she narrowed the distance between them and managed to come "alongside" him (literally or figuratively). The verb catch up in its meaning where it does not take a direct object, and used here in the passive voice.
She caught up to him.
Same underlying meaning as above, verb not taking a direct object, here in the active voice.
He was caught up by her.
Here catch up is used in its transitive meaning and in the passive voice: she brought him "up to speed" on the matter. She gave him the information he lacked. She tutored him or briefed him.
†Compare:
The chair was sat down on (by someone)
Having got off to a good start he was briefly in the lead but was soon caught up to by the other runners.
Do you see how the preposition is carried over when the verb not taking a direct object is used in a passive construction?
Someone sat down on the chair.
The chair was sat down on by someone.
The baby played with the rattle.
The rattle was played with by the baby.
I suppose it's possible to see the verbs there as sit (down) on and play with and then go on to assert that they do take a direct object. But however you want to analyze it, the preposition comes along for the ride in passive constructions using verbs like this.