Can a local government incarcerate homeless people who are a threat to a community?

If by "threat to the community" it is meant that they have violated federal, state, or local laws, yes; it happens daily. If something else is meant, then no. No US Citizen or non-citizen may be arrested or incarcerated in the US unless that person has violated federal, state, or local laws that permit incarceration.

In many parts of the world any government body may arrest and incarcerate oneone at any time without giving a reason. The USA is also guilty of this.