  We consider the chemotaxis-consumption system \[
  \left\{
  \begin{aligned}
  u_t &= \Delta u - \chi \nabla \cdot (u\nabla v) \\
  v_t &= \Delta v - uv
  \end{aligned}
  \right. \] in a smooth bounded domain $\Omega \subseteq \mathbb{R}^n$, $n
\geq 2$, with parameter $\chi > 0$ and Neumann boundary conditions. It is well
known that, for sufficiently smooth nonnegative initial data and under a
smallness condition for the initial state of $v$, solutions of the above system
never blow up and are even globally bounded. Going in a sense a step further in
this paper, we ask the question whether the system can even recover from an
initial state that already resembles measure-type blowup. To answer this, we
show that, given an arbitrarily large positive Radon measure $u_0$ with
$u_0(\overline{\Omega}) > 0$ as the initial data for the first equation and a
nonnegative $L^\infty(\Omega)$ function $v_0$ with \[
  0 < \|v_0\|_{L^{\infty}(\Omega)} < \frac{2}{3n\chi} \] as initial data for
the second equation, it is still possible to construct a global classic
solution to the above system.
