  By a classical theorem of Jordan, every faithful transitive action of a
nontrivial finite group has a derangement (an element with no fixed points).
The existence of derangements with additional properties has attracted much
attention, especially for faithful primitive actions of almost simple groups.
In this paper, we show that an almost simple group can have an element that is
a derangement in every faithful primitive action, and we call these elements
totally deranged. In fact, we classify the totally deranged elements of all
almost simple groups, showing that an almost simple group $G$ contains a
totally deranged element only if the socle of $G$ is $\mathrm{Sp}_4(2^f)$ or
$\mathrm{P}\Omega^+_n(q)$ with $n=2^l \geqslant 8$. Using this, we classify the
invariable generating sets of a finite simple group $G$ of the form $\{ x, x^a
\}$ where $x \in G$ and $a \in \mathrm{Aut}(G)$, answering a question of
Garzoni. As a final application, we classify the elements of almost simple
groups that are contained in a unique maximal subgroup $H$ in the case where
$H$ is not core-free, which complements the recent work of Guralnick and Tracey
addressing the case where $H$ is core-free.
