It's a hard question because the theft was perpetrated by the one person the institution was supposed to be able to trust absolutely. A larger institution could make an attempt at preventing this by not allowing anyone to have unsupervised access to the archives or collections storage, but even this might fail as co-workers tend to get relaxed with one another, or the two people might decide to go in on it together.
There's also a strong tendency to blame the victim in our society. My institution got burglarized last fall. Unbeknownst to any of us (on staff, on the board, or at the security company), some parts of the security system had failed over time. Someone broke a window and stole cash and equipment (including my computer). While we received tremendous support from the community, there were also a lot of comments on web forums and in the newspaper call-in section about how we should've been more careful, we deserved it, etc. etc. So, I think regaining public trust and regard in that setting is pretty difficult too.
I think prevention is the best course of action. Having ethics statements in place, carefully vetting the staff, talking about ethics a lot both within an institution and within the profession, and performing regular inventories all will go a long way towards deterring theft. All of that is easier said than done, though, especially for smaller institutions.
It's actually surprising that this problem isn't more widespread. The majority of the museums in this country don't have anywhere near the staffing, budget or controls of the New York State Library. There are so many tiny places out there with one or two underpaid staff people, no collections security, and in many cases, a lot of unregistered and uncataloged items. The temptation must be overwhelming, yet I do believe that most people rise above it.
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