  We present an optical nebular spectrum of the nearby Type Ia supernova
2011fe, obtained 981 days after explosion. SN 2011fe exhibits little evolution
since the +593 day optical spectrum, but there are several curious aspects in
this new extremely late-time regime. We suggest that the persistence of the
$\sim5800$~\AA\ feature is due to Na I D, and that a new emission feature at
$\sim7300$~\AA\ may be [Ca II]. Also, we discuss whether the new emission
feature at $\sim6400$~\AA\ might be [Fe I] or the high-velocity hydrogen
predicted by Mazzali et al. The nebular feature at 5200~\AA\ exhibits a linear
velocity evolution of $\sim350$ $\rm km\ s^{-1}$ per 100 days from at least
+220 to +980 days, but the line's shape also changes in this time, suggesting
that line blending contributes to the evolution. At $\sim 1000$ days after
explosion, flux from the SN has declined to a point where contribution from a
luminous secondary could be detected. In this work we make the first
observational tests for a post-impact remnant star and constrain its
temperature and luminosity to $T \gtrsim 10^4$ $\rm K$ and $L \lesssim 10^4$
$\rm L_{\odot}$. Additionally, we do not see any evidence for narrow H$\alpha$
emission in our spectrum. We conclude that observations continue to strongly
exclude many single-degenerate scenarios for SN 2011fe.
