Any verb in the plain form (食べる、食べない、食べた、食べなかった, and so on) can be used to modify/describe a noun. I think some verbs might work better in the past form, however:
優れた学生 - a student who has excelled (hard to say who will excel until you have the results)
拗れた話し - a story which has grown complicated (hard to know if/when the story has gotten complicated until you tell it)