A shelling of a polytope $P$ is a linear ordering of facets $F_1, \dots, F_s$ such that for $j>1$, $F_j \cap (\cup_{i<j}F_i)=G_1 \cup \dots \cup G_s$ is the beginning segment of a shelling $G_1, \dots, G_s, \dots, G_r$ of $F_j$. In particular, $F_j \cap (\cup_{i<j}F_i)$ is pure complex, i.e. every face is contained in a facet.
In Ziegler's book lectures on polytopes, lemma 8.10 states that reverse shelling of a polytope is a shelling. I am not completely convinced by his proof.
In the proof, he argues that $F_j \cap (\cup_{i>j} F_i)$ is $G_r \cup \dots \cup G_{s+1}$. I think it is true that $G_r \cup \dots \cup G_{s+1} \subset F_j \cap (\cup_{i>j} F_i)$, but I think it might happen that $F_j \cap (\cup_{i>j} F_i)$ contains some smaller face that is not contained in any of the $G_i$.
Here is a screenshot of Ziegler's proof. Thanks in advance.
Because it's a polytope and not an arbitrary complex, given a facet $F_{i}$, any facet $G$ of $F_{i}$ is shared with exactly one other facet, say $F_{j}$. In the original shelling, either $i<j$ or $j<i$, so if $G$ is already in the complex by the time $F_{i}$ is added, then $F_{j}$ must be in first, so it won't be in the reverse order, and conversely, if it's not in yet when $F_{i}$ is added, then $F_{j}$ must show up later in the order, so it (and $G$) are already in in the reverse order.