Bleed is the word used to describe the region that extends beyond the edges of, let's say, a rectangle.
What is the word used to describe the region that converges towards the center of the rectangle?
"Margin" is the term for the area inset from the trim to the content.
Another term possibly more related to bleed is "Safe area" (or similar). This is often smaller than any margins and is (similar to bleed) usually a small distance specified by the printer as an area to avoid placing content in as it will possibly be trimmed (since trimming is never as precise as we'd like it to be).
Margins are a design and visual consideration whereas any safe area is more of a (as is bleed) technical printing issue.
Note that "margin" is a pretty set term whereas "safe area" is not—I have seen it called many things, but all basically synonymous with "safe area".
There is no opposite term to “bleed” largely because “bleed” is originally and still largely a verb, meaning “to bleed over (the boundary)…” Can you imagine an opposite for that? “Remain within” would not be an opposite. “Shrink into” might and seriously, how would that work in practice?
The correct noun usage is not “bleed” but “bleed area” because the whole point is that it wasn’t measured or considered or in any other way interesting at the design stage.
Anyway “the term” would suggest such a thing applied to print design generally and here we have some thoughts about Indesign particularly. Can we please all acknowledge that Adobe likes to make its own rules, irrespective of what the print design world has accepted for generations?