  Context: As a result of Titan's migration and Saturn's probable capture in
secular spin-orbit resonance, recent works show that Saturn's obliquity could
be steadily increasing today and may reach large values in the next billions of
years. Satellites around high-obliquity planets are known to be unstable near
their Laplace radius, but the approximations used so far are invalidated in
this regime.
  Aims: We aim to investigate the behaviour of a planet and its satellite when
the satellite crosses its Laplace radius while the planet is locked in secular
spin-orbit resonance.
  Methods: We expand on previous works and revisit the concept of Laplace
surface. We use it to build an averaged analytical model that couples the
planetary spin-axis and satellite dynamics.
  Results: We show that the dynamics is organised around a critical point, S1,
at which the phase-space structure is singular, located at 90{\deg} obliquity
and near the Laplace radius. If the spin-axis precession rate of the planet is
maintained fixed by a resonance while the satellite migrates outwards or
inwards, then S1 acts as an attractor towards which the system is forced to
evolve. When it reaches the vicinity of S1, the entire system breaks down,
either because the planet is expelled from the resonance or because the
satellite is ejected or collides into the planet.
  Conclusions: Provided that Titan's migration is not halted in the future,
Titan and Saturn may reach instability between a few gigayears and several tens
of gigayears from now, depending on Titan's migration rate. The evolution would
destabilise Titan and drive Saturn towards an obliquity of 90{\deg}. Our
findings may have important consequences for Uranus. They also provide a
straightforward mechanism for producing transiting exoplanets with a face-on
massive ring, a configuration that is often put forward to explain some
super-puff exoplanets.
