Validated planet candidates need not lie on long-term stable orbits, and instability triggered by post-main-sequence stellar evolution can generate architectures which transport rocky material to white dwarfs, hence polluting them. The giant planet HD 131399Ab orbits its parent A star at a projected separation of about 50-100 au. The host star, HD 131399A, is part of a hierarchical triple with HD 131399BC being a close binary separated by a few hundred au from the A star. Here, we determine the fate of this system, and find the following: (i) Stability along the main sequence is achieved only for a favourable choice of parameters within the errors. (ii) Even for this choice, in almost every instance, the planet is ejected during the transition between the giant branch and white dwarf phases of HD 131399A. This result provides an example of both how the free-floating planet population may be enhanced by similar systems and how instability can manifest in the polluted white dwarf progenitor population.