It's surprising that Webster 1913 does not mention that the word hang has two forms used for the imperfect (past tense), past participle, and the passive voice (and, by consequence, as an adjective). One of them is more rare and has a very specialized use.
Hanged is used exclusively when someone has met their death by hanging: execution, lynching, or suicide.
"During his 21 years on the bench at Fort Smith, Judge Isaac Parker sentenced 160 men to die and hanged 79 of them."
"Of the 1,232 people hanged at Tyburn between 1703 and 1792, only 92 were women."
"The Hanged Man is numbered twelve and is depicted as a figure, usually male, hanging upside down from a tree or branch."
The more common form, "hung", has its own node, and is used everywhere else. It's strange how suspending a human being from a rope uses a different word depending upon where the rope is tied.
"George's teammates were very annoyed when he missed his third field goal in a row. At halftime, they hung him from his locker with athletic tape."
Jennifer was halfway up the face of El Capitan when several of her pitons gave way. She hung desperately from a rope for two hours before finally being rescued."
So, when you recite "A Visit From Saint Nicholas", you do not say
"The stockings were hanged by the chimney with care"
unless, of course, you live with The Addams Family.
Similarly, you do not say
"Hang 'em High begins with Clint Eastwood being hung"
as you are conveying a meaning you probably do not want to convey.