We present a study of high-field transport in carbon nanofibers (CNFs) and breakdown phenomena due to current stress. In situ measurements with scanning transmission electron microscopy reveal that the failure mode of CNFs is strongly related to the morphology of graphite layers comprising CNFs. Comparison with carbon nanotube (CNT) breakdown is made, demonstrating that the current capacity of CNFs is described by a similar model as that of CNTs with a modification of the current capacity of each graphitic layer. The maximum current density is correlated with resistivity, leading to the conclusion that lower resistivity results in higher current capacity in CNFs.