  In this paper, we consider reachability oracles and reachability preservers
for directed graphs/networks prone to edge/node failures. Let $G = (V, E)$ be a
directed graph on $n$-nodes, and $P\subseteq V\times V$ be a set of vertex
pairs in $G$. We present the first non-trivial constructions of single and dual
fault-tolerant pairwise reachability oracle with constant query time.
Furthermore, we provide extremal bounds for sparse fault-tolerant reachability
preservers, resilient to two or more failures. Prior to this work, such oracles
and reachability preservers were widely studied for the special scenario of
single-source and all-pairs settings. However, for the scenario of arbitrary
pairs, no prior (non-trivial) results were known for dual (or more) failures,
except those implied from the single-source setting. One of the main questions
is whether it is possible to beat the $O(n |P|)$ size bound (derived from the
single-source setting) for reachability oracle and preserver for dual failures
(or $O(2^k n|P|)$ bound for $k$ failures). We answer this question
affirmatively.
