Should homeless individuals, that have refused available shelter or housing, be allowed to sleep or encamp on public property?

No. Make it a criminal offense requiring community service.

If the person that owns the property says yes then its fine.

only on certain public propertys

Regardless, should be decided by the state.

Yes but only on public property set aside for that purpose. It should not be allowed if it is impacting the publics ability to use the property for its intended use.

yes, as long as it is not disturbing anyone or anything.

Only if there was reason for them to not want to stay the shelter

Individuals have a right to traverse and loiter on public property, regardless of whether they are homeless or not, so long as they are not damaging property or otherwise depriving the rest of the public of their ability to enjoy those spaces safely. Large groups of people creating "pop-up villages" within a space not designed and designated for the purpose create a hazard for those living there, deprive the rest of the general public of its use of the property, and can create an undue and unintended burden on surrounding infrastructure. I support the rights of individuals to traverse and loiter as well as the rights of local governments to protect public assets and ensure public safety.

No, but create more social programs to provide free food, clothing and medicine as well as better and safer shelters as current are not at all "safe" spaces, which is why many refuse to stay.

If they aren't creating a disturbance to others, actively engage in improving or maintaining the property, then I don't see an issue with their presence.

Yes, but not public property within city limits.