>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.

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†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.