The way the Time Remnants work got a bit better of an explanation in the finale - it was a bit of a mess when first explained. let's see if I can put it on paper, virtually speaking.
Scenario one - If a person goes back in time to a point in their past, there would be two of them at one point in the timestream. Theoretically, if they never interacted, time would proceed as it did before, to the point when said character made the trip into the past. At that point, there would be only one version of that character again, with full memory of his entire trip. Such a trip would have little effect on the timeline, presuming said character made no other major changes in other areas.
In scenario two, the character interacts with himself in the past in some way, giving him knowledge that he will need, and also letting him know that at some point in the future, he will go back into time. This is the scenario we saw in Flash Back - the timeline was changed in that Pied piper did not die, and became an ally of the team. But at the end of the series of events, we're still left with only one version of said character, possibly with knowledge of both the original and changed timeline.
The Time Remnant is a third scenario, possibly only doable by a speedster. The speedster travels to the past, and interacts with his past self. He convinces past self to engage in a series of actions wildly different from the original timeline, while the time-travelling speedster takes his place in the timeline. At this point that "original" version breaks off from the timeline - imagine a looped piece of string, knotted together, and the loop cut off to create a second, smaller, piece of string. This results in TWO concurrent versions of the character, up until the moment one of them dies.
This third scenario is FAR more of a blow to the fabric of reality, and one more likely to cause the Time Wraiths / Black Flashes to appear. Barry's creation of a remnant resulted in the Black Flashes to appear, but as he said, they saw Zoom was a far greater threat to reality, and took him instead.
In answer to the commenter's question, it seems that once the remnant is "created" either one could die. The event that created the remnant has already happened. We're not talking about a character from "the future" here, but one from our present that travels to the past. So a death in the present would not affect the future.