  ${\textbf{Background:}}$ Atomic nuclei often exhibit collective
rotational-like behavior in highly excited states, well above the particle
emission threshold. What determines the existence of collective motion in the
continuum region, is not fully understood.
  ${\textbf{Purpose:}}$ In this work, by studying the collective rotation of
the positive-parity deformed configurations of the one-neutron halo nucleus
$^{11}$Be, we assess different mechanisms that stabilize collective behavior
beyond the limits of particle stability.
  ${\textbf{Method:}}$ To solve a particle-plus-core problem, we employ a
non-adiabatic coupled-channel formalism and the Berggren single-particle
ensemble, which explicitly contains bound states, narrow resonances, and the
scattering continuum. We study the valence-neutron density in the intrinsic
rotor frame to assess the validity of the adiabatic approach as the excitation
energy increases.
  ${\textbf{Results:}}$ We demonstrate that collective rotation of the ground
band of $^{11}$Be is stabilized by (i) the fact that the $\ell=0$ one-neutron
decay channel is closed, and (ii) the angular momentum alignment, which
increases the parentage of high-$\ell$ components at high spins; both effects
act in concert to decrease decay widths of ground-state band members. This is
not the case for higher-lying states of $^{11}$Be, where the $\ell=0$
neutron-decay channel is open and often dominates.
  ${\textbf{Conclusion:}}$ We demonstrate that long-lived collective states can
exist at high excitation energy in weakly bound neutron drip-line nuclei such
as $^{11}$Be.
