By now 12 Monkeys has cleverly added a few more time-travel ingredients to the mix, which make it a very interesting case of time-travel story. We had already established that the main "mode" of time travel is the one that produces changes in history "on the fly".
In addition to a perfect closed loop (chapter 4), we now have seen some degree of "self-healing", as the minor changes caused by the very presence of the time-travelers in the past (2015/2016; 1987) clearly do not have any effect on the present: the plague has still happened and the team is still trying to stop it from happening via time-travel.
We have also seen an intervention that did have an effect (Cassie dies, the plague still happens, but the present world is even worse) and that is "undone" . This is obviously a very unlikely possibility: to "undo" the changes they travel to the past and cause "major", lasting changes again - what are the odds of the outcome being the same original history, and not a different one?
We have learned that the version of history we are seeing already incorporates a major closed loop: Cole is chosen to be sent to the past by Jones because she met his time-traveling version when she was young and therefore knows she would chose him eventually. Also, the message that made them travel to the past in the first place is a recording from Cassie in which she does mention Cole, so, again, the events in the past incorporate Cole's presence. It is this version of history, with its closed loop(s), what they are trying to change.
And in chapter 2 of season 2 they finally manage to do this. At this point 12 Monkeys again surprises by addressing, instead of ignoring, the question of which version of the travelers (and the people involved in making the jumps possible) are found in the new history. They incorrectly expected to disappear, but they find their same selves (instead of duplicates of the actual travelers) in the new history. However, they explain it in a clever way: all involved in time travel remain the "original" selves, with the memories of the original timeline and, - this is a commendable difference from other shows- no memory of the new history, which they have to learn from scratch, as for example Jones's discovery that she is married to an unknown colleague scientist!