In small town America, such things beg the creation of vigilance organizations. But it requires some strict prerequisites.
1) The government either does not take the side of the public against offenders; or worse, takes the side of the offenders against the public.
2) Typically, vigilance organizations try to follow all the rules, but if their efforts at petition, election, prosecution and strict punishment are ignored; even then they try to remain peaceful until they are forced to take the law into their own hands.
3) The nature of the offender, the victim, and the offense matter greatly. In this case, all three can cause rapid development of a vigilance organization.
The town had attracted a large criminal element about 1880 due to its easy access to another jurisdiction where the Arkansas authorities couldn't touch them and benign neglect by a federal government which considered them too remote and low on the priority list.
This changed by mid-decade as authorities who weren't particularly concerned about the safety of the townspeople did become concerned about the activity of roving vigilante gangs, especially when they hung the wrong man a time or two. Clint Eastwood's classing Hang 'em High was based on this era.
Once the authorities stepped up to the plate and did what they should have done in the first place, the vigilante gangs melted away.
Within 15 years, Fort Smith transformed from a Mecca of crime into a nice little town of frame houses and church goers. The town gallows, which had played a key role in that remarkable transformation, was taken down.