Have you ever been to community theatre where theatrical performances are made up and performed by the community?
No, I have never heard of that. Are the performances good? 
I would imagine that would have a lot to do with the community! lol Many community groups are non-profit business with large memberships and even have a work staff.
Oh wow! Where would I find out if they do this in my area?
I would look online for resources. Many theatres are small groups that perform in borrowed spaces and others are large groups that have permanent facilities.