If Captain Braxton in Future's End never experienced the timeline where he goes back in time, why does he try to stop it in Relativity?

Question

Captain Braxton returns through the rift in “Future's End” having never experienced the catastrophic destruction of the solar system time line, which has been altered. Then in season 5, "Relativity" his far future self plants a device to destroy Voyager to prevent himself from going back to the timeline which no longer exists. Where does the Braxton come from and how was the causality loop even broken in “Future's End”?

BRAXTON: Yes. No. Yes. That's the paradox, my dear. A leads to B leads to C leads to A. Juvenile minds. Oh, how can I make you understand, huh? A. There's an explosion in the twenty ninth century. Debris from Voyager's hull is found in evidence. I go back in time to destroy you. B. You try to stop me, disabling my weapon which causes me to crash-land back here in the twentieth century. C. Someone in this century steals my timeship and launches it. They go into the future and once there they make one critical mistake which causes a terrible explosion that takes us all the way back to A. There's an explosion in the twenty ninth century. The cycle of causality is complete.

So there are two questions. How does Voyager break the causality loop and not repeat the same events that resulted in Voyager's remains being found in the wreckage, and where does crazy future Braxton come from in "Relativity"? If he came from the 20th century homeless man, then how does he get off earth?

Answer 1

Time travels and time paradoxes are handled slightly differently in each series of the ST. Unfortunately.

As for second question - crazy Braxton is the result of several Voyager timeline incursions. It is the older version of the current captain of the USS Relativity. It is helpful to think in somewhat non-linear way about him. He's the product of changing and then restoring timeline(s), but he's necessarily outside the causality loop. I think the Ducane's phrase about them being reintegrated with their past selves when talking to Seven and Janeway (and he also incuded Braxton in that sentence) explains the problem somewhat, too.

As for causality loop break and not destroying future star system... Only explanation I have is that thinking about those things as a loop is wrong. It's more like an iteration, because yes, every time something happens to change the timeline (which is also creating it's own branch of reality, as explained in one of the episodes of the TNG), there is a factor that is aware of the outcome of the previous loop.

Also, plot device and somewhat lazy screenwriters.

In case it's confusing, see Loki's comment to the question itself.