1911 Encyclopedia Britannica
The nickname for vagrants who infested England in Tudor times. The phrase is certainly as old as 1561, and was due to these beggars pretending that they were patients discharged from the Abraham ward at Bedlam. The genuine Bedlamite was allowed to roam the country on his discharge, soliciting alms, provided he wore a badge. This humane privilege was grossly abused, and thus gave rise to the slang phrase "to sham Abraham."
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Chisholm, Hugh, General Editor. Entry for 'Abraham-Men'. 1911 Encyclopedia Britanica. https://www.studylight.org/encyclopedias/eng/bri/a/abraham-men.html. 1910.