Ages ago before some of these discussions went off the rails I asked the era when the burials occurred, and I don’t think there was ever an answer for it. If it was in the late 70s when I think the last of these ceased operations, that would raise a lot of questions. If it was in the 1890s, somewhat less.
In the 19th century most people were buried near where they died (whether it be at home or not) due to the logistics of the era in transporting bodies, and most people not having the means to arrange for that. It wouldn’t surprise me if any facility in which large numbers of people lived had burial facilities nearby.
I’ve visited this Asylum (after closing it became a tourist attraction): Weston State Hospital Cemetery in Weston, West Virginia - Find A Grave Cemetery
Note that it just says there’s a single market there to commemorate everyone buried. They buried lots of people there over its years of operation, but they were always buried in “temporary marked” graves (not unmarked.) The temporary markers were cheap and made of wood, and over time disappeared.