When an electron emitting tip is subjected to very high electric fields, plasma forms even under ultra high vacuum conditions. This phenomenon, known as vacuum arc, causes catastrophic surface modifications and constitutes a major limiting factor not only for modern electron sources, but also for many large-scale applications such as particle accelerators, fusion reactors etc. Although vacuum arcs have been studied thoroughly, the physical mechanisms that lead from intense electron emission to plasma ignition are still unclear. In this article, we give insights to the atomic scale processes taking place in metal nanotips under intense field emission conditions. We use multi-scale atomistic simulations that concurrently include field-induced forces, electron emission with finite-size and space-charge effects, Nottingham and Joule heating. We find that when a sufficiently high electric field is applied to the tip, the emission-generated heat partially melts it and the field-induced force elongates and sharpens it. This initiates a positive feedback thermal runaway process, which eventually causes evaporation of large fractions of the tip. The reported mechanism can explain the origin of neutral atoms necessary to initiate plasma, a missing key process required to explain the ignition of a vacuum arc. Our simulations provide a quantitative description of in the conditions leading to runaway, which shall be valuable for both field emission applications and vacuum arc studies.