。
She was very nearly run over by a truck.
Literal
She [topic-は] just-barely [at-で] truck [by-に] be-run-over was-about-to.
A double 'near miss' frame: すんでのところで (literally 'right at the brink') and ~ところだった ('was about to / was on the verge of') both signal an event that almost happened but didn't. すんで is an old word for the very edge of an event, surviving in modern Japanese mainly inside this fixed phrase. The combination is pleonastic but emphatic — the same as English doubling up 'just barely' with 'almost'. The verb ひかれる is the passive of 轢く ('run over with a vehicle'), and the に marks the agent (the truck). The whole sentence captures a heart-stopping close call.