  We study the isotropic Quot schemes $IQ_e (V)$ parameterizing degree $e$
isotropic subsheaves of maximal rank of an orthogonal bundle $V$ over a curve.
The scheme $IQ_e (V)$ contains a compactification of the space $IQ^o_e (V)$ of
degree $e$ maximal isotropic subbundles, but behaves quite differently from the
classical Quot scheme, and the Lagrangian Quot scheme in [6]. We observe that
for certain topological types of $V$, the scheme $IQ_e (V)$ is empty for all
$e$. In the remaining cases, for infinitely many $e$ there are irreducible
components of $IQ_e (V)$ consisting entirely of nonsaturated subsheaves, and so
$IQ_e (V)$ is strictly larger than the closure of $IQ^o_e (V)$. As our main
result, we prove that for any orthogonal bundle $V$ and for $e \ll 0$, the
closure $\overline{IQ^o_e (V)}$ of $IQ^o_e (V)$ is either empty or consists of
one or two irreducible connected components, depending on $\deg(V)$ and $e$. In
so doing, we also characterize the nonsaturated part of $\overline{IQ^o_e (V)}$
when $V$ has even rank.
