This is the 10877th most frequent Russian word.
выпавшую
The Russian word "выпавшую" means "fallen" or "that has fallen" (feminine, accusative form).
In this sentence, 'выпавшую' is the feminine singular accusative form of the participle 'выпавший', which comes from the verb 'выпасть' (to fall out). It describes the page that has fallen out.
Он осторожно подобрал выпавшую страницу из книги.
He carefully picked up the fallen page from the book.
Here, 'выпавшую' again is a participle describing 'одежду' (clothes), indicating that the clothes had a prior action of falling off the line.
Выпавшую одежду с верёвки унесло ветром.
The clothes that had fallen from the line were carried away by the wind.
In this sentence, 'выпавшую' describes 'деталь' (part), denoting that this part had previously fallen out of the machine.