I'm not sure where you live, but most cemeteries have 'PLOTS" or "Sections" and then a "Grave Number"..they usually have several area's where the "Indigent" are buried, but not in the same 'GRAVE". I would imagine that the public grave that you are talking about would mean that they are in a seperate section....but different graves. I think exceptions might be made during an epidemic, but on the other hand, maybe I mis-understood your post.
It would be rare for "one big hole" to be dug for multiple graves, I would think. An exception to that might be when cemeteries are moved ....and unmarked graves can be re-buried....I don't know the answer to that. (That did happen during the Civil War)
I also have heard that sometimes indigents (or unknowns) are buried same grave, but stacked one atop another. Not sure if that would apply to all states, tho. Some cemeteries DO have a seperated SECTION for burial for indigent.
I happen to know, that can be arranged at SOME cemeteries, where a husband dies, and then the wife..they just dig the hole deeper, and then bury the last to die on top. Markers can be installed as well, if family pays for that. Unfortunately different states and cemeteries have different rules, since some are privately owned and some are public cemeteries. Some cemeteries "back when" had no rules, so who can tell about that time period.
You should inquire if there are seperate GRAVE PLOTS......NOT JUST THE "PLOT" NUMBER.