A popular trope in westerns is that of the public hanging, often as a setup for the protagonist to either rescue a compatriot or themselves be rescued.
Is there any basis in fact for public hangings in the early frontier communities of the old west? Or were they mostly carried out in private?
My understanding is that most hangings would have involved trees or wagons since the “trapdoor” method wasn’t common until the 1870s.
Likewise, are there any examples of a person being rescued from a hanging?
There were two species of hangings that occurred in the American West: lynchings implemented by "vigilance" committees and legally sanctioned executions. Both had public and more private manifestations.
Vigilance committees often operated under cover of darkness and in secrecy to conceal the identities of participants so they would not face murder charges. That said, the San Francisco executions of the 1850s famously were extremely public with hundreds of "executioners" in attendance making prosecution if not impossible, not likely. Whether public or otherwise, the committees sought to make their activity well know to intimidate the "bad elements" of society and to impose their own power so their influence would be felt.
In the case of legally sanctioned executions, these were often held within penitentiaries with limited public viewing. As today, it was better for security purposes to escort a criminal to the gallows within the walls of the facility. Early on, this was not always the process that was followed, but in general, it was.
There were two public, legally sanctioned executions in Virginia City, Nevada, one in 1868 and the other in 1877. Both were hangings with purpose-built wooden gallows with trap doors. The first of these was attended by approximately 4,000 people who brought picnic lunches. Mark Twain was one of those attended, and he was nauseated by the spectacle, writing about the event and subsequently maintaining a life-long opposition to capital punishment as a result of what he saw. I write about the case in my article, "Sex, Murder, and the Myth of the Wild West: How a Soiled Dove Earned a Heart of Gold".
The second hanging occurred in front of the place where the crime was committed: a murder in a saloon along the notorious "Barbary Coast" of Virginia City. In this case, the city fathers wanted to send a message to the "Coast" that it WOULD be cleaned up, and the hanging had a chilling effect on those who conducted business there, inspiring many to retreat to the city-sanctioned red light district.
These public hangings were oddities, in general, since, as indicated, executions were usually within the confines of penitentiaries. I have never heard of a legally sanctioned execution being challenged by anyone - let alone with a successful rescue of the condemned.