IN this story, it appears that Syme ends up getting killed. We do not know this for absolutely sure, but it seems like it must have happened.
First of all, Winston is absolutely sure that Syme will end up getting killed. That is because Syme is clearly too smart to stay alive in this society. He thinks too much and has too much insight. So that implies he's going to die.
At the start of Chapter 8, Syme is gone from work. And his name is gone from the list of people on the chess club. That implies he is dead.
Then, at start of Part 2, Chapter 6, O'Brien seems to confirm it by talking about Syme to Winston, but saying he does not remember his name. This implies that Syme has become an unperson -- that he never officially existed.