Learn Finnish: Näimme langenneet ja tuomitut metsässä. - We saw the fallen and the condemned in the forest.

They are "substantivized" participles, which means they are being used directly as nouns rather than as adjectives describing something else. Instead of saying langenneet ihmiset (the fallen people), we can drop the noun and just say langenneet (the fallen ones / those who have fallen). The same applies to tuomitut (the condemned ones).

What is the grammatical difference between langenneet and tuomitut?

Langenneet is a past active participle (the NUT-participle), meaning these people did the action themselves—they fell. Tuomitut is a past passive participle (the TU-participle), meaning the action was done to them by someone else—they were condemned.

Why does the participle for langeta (to fall) look like langenneet?

Langeta is a Type 6 verb (like paeta or vaieta). To form the past active participle for this verb type, you remove the -ta ending and add -nnut or -nnyt, resulting in langennut for the singular. Because this sentence is about a plural group, the plural ending makes it langenneet.

If they are the object of näimme, why aren't they in the partitive or the accusative -n case?