  The asymptotically autonomous robustness of random attractors of stochastic
fluid equations defined on \emph{bounded} domains has been considered in the
literature. In this article, we initially consider this topic (almost surely
and in probability) for a non-autonomous stochastic 2D Navier-Stokes equation
driven by additive and multiplicative noise defined on some \emph{unbounded
Poincar\'e domains}. There are two significant keys to study this topic: what
is the asymptotically autonomous limiting set of the time-section of random
attractors as time goes to negative infinity, and how to show the
precompactness of a time-union of random attractors over an \emph{infinite}
time-interval $(-\infty,\tau]$. We guess and prove that such a limiting set is
just determined by the random attractor of a stochastic Navier-Stokes equation
driven by an autonomous forcing satisfying a convergent condition. The uniform
"tail-smallness" and "flattening effecting" of the solutions are derived in
order to justify that the usual asymptotically compactness of the solution
operators is \emph{uniform} over $(-\infty,\tau]$. This in fact leads to the
precompactness of the time-union of random attractors over $(-\infty,\tau]$.
The idea of uniform tail-estimates due to Wang \cite{UTE-Wang} is employed to
overcome the noncompactness of Sobolev embeddings on unbounded domains. Several
rigorous calculations are given to deal with the pressure terms when we derive
these uniform tail-estimates.
