The solid, central part of a comet-its nucleus-is subject to destructive processes(1,2), which cause nuclei to split at a rate of about 0.01 per year per comet(3). These destructive events are due to a range of possible thermophysical effects(4); however, the geophysical expressions of these effects are unknown. Separately, over two-thirds of comet nuclei that have been imaged at high resolution show bilobate shapes(5), including the nucleus of comet 67P/Churyumov-Gerasimenko (67P), visited by the Rosetta spacecraft. Analysis of the Rosetta observations suggests that 67P's components were brought together at low speed after their separate formation(6). Here, we study the structure and dynamics of 67P's nucleus. We find that sublimation torques have caused the nucleus to spin up in the past to form the large cracks observed on its neck. However, the chaotic evolution of its spin state has so far forestalled its splitting, although it should eventually reach a rapid enough spin rate to do so. Once this occurs, the separated components will be unable to escape each other; they will orbit each other for a time, ultimately undergoing a low-speed merger that will result in a new bilobate configuration. The components of four other imaged bilobate nuclei have volume ratios that are consistent with a similar reconfiguration cycle, pointing to such cycles as a fundamental process in the evolution of short-period comet nuclei. It has been shown(7,8) that comets were not strong contributors to the so-called late heavy bombardment about 4 billion years ago. The reconfiguration process suggested here would preferentially decimate comet nuclei during migration to the inner solar system, perhaps explaining this lack of a substantial cometary flux.