OK let me find you a pic or two. that round washer looking thing goes to a fender or rack mount. the hook or 'claw' on the rear derailleur goes on the outside of the frame but under that mount hardware.
there should have been a small bolt and weird looking nut to hold the derailleur in the dropout slot.
the derailleur should not come off simply because the wheel was removed.
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“One morning you wake up, the girl is gone, the bikes are gone, all that's left behind is a pair of old tires and a tube of tubular glue, all squeezed out"
Sugar "Kane" Kowalczyk