Thin enough black strings are unstable to growing ripples along their length, eventually pinching and forming a naked singularity on the horizon. We investigate how string theory can resolve this singularity. First, we study the string-scale version of the static non-uniform black strings that branch off at the instability threshold: “string-ball strings”, which are linearly extended, self-gravitating configurations of string balls obtained in the Horowitz-Polchinski (HP) approach to
near-Hagedorn string states. We construct non-uniform HP strings in spatial dimensions d ≤ 6 and show that, as the inhomogeneity increases, they approach localized HP balls. We find that, for a sufficiently small mass, the uniform HP string will be stable and not evolve into a non-uniform or localized configuration. Building on these results and independent evidence from
the evolution of the black string instability with α' corrections, we propose that, at least in d = 4, 5, string theory slows and eventually halts the pinching evolution at a classically stable stringy neck. In d ≥ 6 this transition is likely to occur into a puffed-up string ball. The system then enters a slower phase in which the neck gradually evaporates into radiation. We discuss this scenario as a framework for understanding how string theory resolves the formation of naked singularities.