= Solution
Let $G=\gamma_I\Sigma_f\phi$ be the constant precursor production rate per volume. Here $\gamma_I$ is the precursor yield per <nuclear fission>, and $I$ and $X$ are <number densities>. At a <steady state>,
$$
I_0=\frac{G}{\lambda_I},
\qquad
X_0=\frac{G}{\lambda_X+\phi\sigma_{aX}}.
$$
For fixed homogeneous coefficients and spatial shape, the reactivity contribution of an added absorption coefficient $\Sigma_{aX}=\sigma_{aX}X_0$ is $-\Sigma_{aX}/(\nu\Sigma_f)$. Thus the model gives
$$
\Delta\rho_X
=-\frac{\gamma_I}{\nu}
\frac{\phi\sigma_{aX}}{\lambda_X+\phi\sigma_{aX}}.
$$
When capture removal dominates xenon <radioactive decay>, $\phi\sigma_{aX}\gg\lambda_X$, and hence
$$
\boxed{\Delta\rho_X\longrightarrow-\frac{\gamma_I}{\nu}.}
$$
The limit is independent of the xenon <neutron absorption cross section>: at high <neutron flux>, nearly every xenon atom supplied by the precursor ultimately consumes a <neutron>. The assumptions include constant pre-shutdown <neutron flux>, sufficient time for precursor and xenon equilibrium, the supplied single-precursor model with no direct xenon fission source, and fixed parameters for translating absorption into <reactor reactivity>.
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