。
She told her child to finish their food.
Literal
She [topic-は] child [target-に] food [object-を] finish-eating [so as to-ように] told.
An indirect command built on ~ように言う: the embedded clause 食べ物を食べてしまう describes what's commanded, ように nominalizes that as 'such that they X,' and 言った reports the speech act. ~てしまう here is the completive sense — 'eat all the way through, finish up' — a parental nudge to clean the plate rather than a regretful 'unfortunately ate.' A live version of the command might sound like 食べ物を全部食べてしまいなさい ('finish all your food!').