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The loss of two MOBA works to theft has drawn media attention and enhanced the museum's stature.In 1996, the painting Eileen, by R. Angelo Le, vanished from MOBA. Eileen was acquired from the trash by Wilson, and features a rip in the canvas where someone slashed it with a knife even before the museum acquired it, "adding an additional element of drama to an already powerful work", according to MOBA.

The museum offered a reward of $6.50 for the return of Eileen, and although MOBA donors later increased that reward to $36.73, the work remained unrecovered for many years. The Boston Police listed the crime as "larceny, other", and Sacco was reported saying she was unable to establish a link between the disappearance of Eileen and a notorious heist at Boston’s famed Isabella Stewart Gardner Museum that occurred in 1990. In 2006—10 years after Eileen was stolen—MOBA was contacted by the purported thief demanding a $5,000 ransom for the painting; no ransom was paid, but it was returned anyway.

Prompted by the theft of Eileen, MOBA staff installed a fake video camera over a sign at their Dedham branch reading: "Warning. This gallery is protected by fake video cameras". Despite this deterrent, in 2004 Rebecca Harris' Self Portrait as a Drainpipe was removed from the wall and replaced with a ransom note demanding $10, although the thief neglected to include any contact information. Soon after its disappearance the painting was returned, with a $10 donation. Curator Michael Frank speculates that the thief had difficulty fencing the portrait because "reputable institutions refuse to negotiate with criminals."