The noteworthy four-planet HR 8799 system teeters on the brink of gravitational instability and contains an A-type host star which is characteristic of the progenitors of the majority of known white dwarf planetary system hosts. Gozdziewski & Migaszewski (2020) have demonstrated that the system can retain all four planets for at least 1 Gyr along the main sequence if the planets evolve within an externally unperturbed 8:4:2:1 mean motion resonance configuration. Here we propagate forward their most stable fit beyond the main sequence, and incorporate external effects from Galactic tides and stellar flybys. We find that (i) giant branch mass loss always breaks the resonance, and usually triggers the ejection of two of the planets, (ii) stellar flybys and Galactic tides rarely break the resonance during the main-sequence and giant branch phases, but play a crucial role in determining the final planetary configurations around the eventual white dwarf host star, and (iii) the meanderings of the surviving planets vary significantly, occupying regions from under 1 au to thousands of au. The ubiquitous survival of at least one planet and the presence of the debris discs in the system should allow for dynamical pathways for the white dwarf to be metal-polluted.