What could we learn from a sharply falling positron fraction?

Recent results from the AMS-02 data have confirmed that the cosmic ray positron fraction increases with energy between 10 and 200GeV. This quantity should not exceed 50%, and it is hence expected that it will either converge towards 50% or fall. We study the possibility that future data may show the positron fraction dropping down abruptly to the level expected with only secondary production, and forecast the implications of such a feature in term of possible injection mechanisms that include both dark matter and pulsars. {Were a sharp steepening to be found, rather surprisingly, we conclude that pulsar models would do at least as well as dark matter scenarios in terms of accounting for any spectral cut-off.