Do the Dead Sea scrolls describe any prophecy which was fulfilled after they were written? Is there any manuscript among the Dead Sea scrolls, which foretold something that happened after the manuscript was written?
Yes!

The Dead Sea Scrolls are not themselves a unique set of content, but rather a collection --rather like someone's private library-- of various texts from the time period that were all preserved together and help us understand the state of those texts at a specific point in time.

One example would be the Isaiah scroll, a basically complete copy of the entire book of Isaiah in one place. The book of Isiah was written ~750 years before Christ and includes many specific descriptions of what is life, dead and resurrection would be like.


  Isaiah 53:7-9 (ESV)
  He was oppressed, and he was afflicted,
  yet he opened not his mouth;
  like a lamb that is led to the slaughter,
  and like a sheep that before its shearers is silent,
  so he opened not his mouth.
  By oppression and judgment he was taken away;
  and as for his generation, who considered
  that he was cut off out of the land of the living,
  stricken for the transgression of my people?
  And they made his grave with the wicked
  and with a rich man in his death,
  although he had done no violence,
  and there was no deceit in his mouth.  


You can see these verses on the scroll here. If you are interested there are lots of commentaries available on the hundreds of specific things Isaiah foretold about the Messiah that were fulfilled in the person of Jesus.

Also be aware that other works besides canonical scriptural texts were among the scrolls found. There are other works from the time period. The find has no particular affect on what text are or are not considered scripture any more than looking at the titles in a pastor's library today would prove one way or another what he believed, but the quality and quantity of texts found together do provide collaborative evidence for the integrity of other copies of the texts that were found elsewhere and in smaller chunks.