I vaguely remember an article made by, I believe it was "In-Fisherman Magazine", in the 1980's on this very subject. Can a bass lake be fished out. In a nutshell and briefly as I can get the gist of the article across. Here is the story as best as I can remember.
A private lake about 100 acres was to be fished by some professional fishermen and selected others. The catch was they had to record everything about the fish and method used and tag every bass caught. Well they started this experiment in the spring. By mid summer they were catching a lot of bass with tags in them. As fall approached they started to catching a lot of bass without tags. The consensus was there was a population of bass that stayed deep all summer after the spawn. Only to be caught as the water cooled in the fall. The following year very few untagged bass were caught. The experiment concluded that yes a population of bass could be caught down to an unfishable population. This information supported the "catch and release" tournaments.
I might add that possession limits are for a reason and obeying them is good advice for the population and your wallet. TWRA loves to catch fishermen over the limit.