The people means what it says. It is everyone. That's why we have to hold a hearing before deporting someone. It has nothing to do with citizen. We can't go by implied. If they meant citizens that would have said so.
No, the people doesn't have anything to do with an individual. it has to do wit the whole of the people. Person is the individual. The writers seemed to be very careful how they worded things except for the 2nd Amendment. Maybe they thought that comma didn't change anything or mean anything.