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 lines 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.
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