= Solution
For slow mass loss, the <adiabatic invariance of an orbital action> applies. Spherical symmetry conserves $L$ exactly, and adiabatic evolution conserves the radial action. For a Kepler orbit,
$$
J_r+L=\sqrt{GMa}.
$$
Consequently $Ma$ and $e$ remain constant. When the central mass halves, every semimajor axis doubles while each eccentricity is unchanged:
$$
\boxed{a_1=2a_0,
\qquad e_1=e_0}.
$$
No orbit becomes unbound as long as the final mass remains positive, so
$$
\boxed{f_{\rm unbound}=0}.
$$
Because the action mapping changes no eccentricity and introduces no orientation preference, the initially isotropic distribution remains isotropic rather than becoming radially or tangentially anisotropic.
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