Although 25–50 per cent of white dwarfs (WDs) display evidence for remnant planetary systems, their orbital architectures and overall sizes remain unknown. Vibrant close-in (≃1 R⊙) circumstellar activity is detected at WDs spanning many Gyr in age, suggestive of planets further away. Here we demonstrate how systems with 4 and 10 closely packed planets that remain stable and ordered on the main sequence can become unpacked when the star evolves into a WD and experience pervasive inward planetary incursions throughout WD cooling. Our full-lifetime simulations run for the age of the Universe and adopt main-sequence stellar masses of 1.5, 2.0 and 2.5 M⊙, which correspond to the mass range occupied by the progenitors of typical present-day WDs. These results provide (i) a natural way to generate an ever-changing dynamical architecture in post-main-sequence planetary systems, (ii) an avenue for planets to achieve temporary close-in orbits that are potentially detectable by transit photometry and (iii) a dynamical explanation for how residual asteroids might pollute particularly old WDs.