Is a terminal symplectic variety S_4? For purposes of this question "terminal symplectic variety" means a normal variety which is symplectic (in the usual sense of symplectic singularities) and whose singular locus has codimension $\geq 4$ (the equivalence of this with the usual definition of terminal is a theorem of Namikawa).  
Symplectic varieties has lots of nice properties; For example, they are always Cohen-Macaulay, which is a condition about niceness with respect to depth.  So, one can hope for others.

Is a terminal symplectic variety necessarily $S_4$?

I should warn any potential answerers that my understanding of the $S_4$ property is very poor (it's an exceptionally tough thing to Google, since it's not even the dominant use of that term in mathematics). I hesitate to even give a definition for fear of messing it up;  I believe it means that every ideal sheaf of codimension $\leq 3$ has depth equal to its codimension. 
 A: I'm posting this as an answer due to encouragement to do so from Noah Snyder in the comments.
As mentioned above in my comment.  A ring $R$ is ${\text{S}}_n$ if for every prime ideal $\mathfrak{q} \subseteq R$, $R_q$ has depth at least $\text{min}(\dim R_{\mathfrak q}, n)$.
A ring is Cohen-Macaulay if the depth of each $R_{\mathfrak{q}}$ is equal to $\dim R_{\mathfrak q}$.  Thus a ring is Cohen-Macaulay if and only if it is $\text{S}_n$ for every $n$.  In particular, any terminal, or even log terminal singularity is Cohen-Macaulay and thus also $\text{S}_4$.
Log canonical singularities don't satisfy this property (they need to be Cohen-Macaulay).  However, if you have a family of varieties with log canonical singularities say over a smooth curve, the $\text{S}_n$ property is is closed (in particular, a limit of $\text{S}_n$ varieties is $\text{S}_n$).  See the paper of Kollar-Kovacs, HERE
A: Ben,
a terminal singularity is Cohen-Macaulay and Cohen-Macaulay implies $S_n$ for all $n$.
By the way, I already mentioned this in my answer to your previous question about this issue. (here).
