ABSTRACT White dwarfs containing orbiting planetesimals or their debris represent crucial benchmarks by which theoretical investigations of post-main-sequence planetary systems may be calibrated. The photometric transit signatures of likely planetary debris in the ZTF J0139+5245 white dwarf system have an orbital period of about 110 d. An asteroid which breaks up to produce this debris may spin itself to destruction through repeated close encounters with the star without entering its Roche radius and without influence from the white dwarf’s luminosity. Here, we place coupled constraints on the orbital pericentre (q) and the ratio (β) of the middle to longest semiaxes of a triaxial asteroid which disrupts outside of this white dwarf’s Roche radius (rRoche) soon after attaining its 110-d orbit. We find that disruption within tens of years is likely when β ≲ 0.6 and q ≈ 1.0–2.0rRoche, and when β ≲ 0.2 out to q ≈ 2.5rRoche. Analysing the longer time-scale disruption of triaxial asteroids around ZTF J0139+5245 is desirable but may require either an analytical approach relying on ergodic theory or novel numerical techniques.