Lots of productive wildlife harvest methods incorporate a "hands off" area that then provides a steady supply of immigrants to surrounding habitat where they can be harvested. They tend to be fairly stable units as a result.
There are lots of examples at lots of scales, from Marine systems that are in hundreds of miles to quite small wildlife refuges (esp. waterfowl, here in Iowa) that are only hundreds of acres. Whether this works with sheep in southern AZ, I cannot say, but it would not surprise me if it was such a functional system.
You could even think of Yellowstone elk and bison as being somewhat similar in this regard. And of course, anyone that has ever set up on the boundary of an unhuntable park or refuge, waiting for those especially big bucks to venture out, has seen this in a microcosm.
Anyway, just speculating out loud. It would be interesting to test this, but, alas, we are running out of USFWS and Park biologists of all stripes.