Everyone who had seen the Deer Head would have a virus named "Deer Head" implanted in their brain. That virus itself was part of the Deer Head, an avatar of hers.
It was the key to opening the "Anywhere Door" at any time and place, which was also the escape ability most crucial for the survival of the Babel's executives. As long as they were not targeted for assassination or killed silently, they could almost always escape if there was even slight room to maneuver.
Because the Deer Head only had a half-broken body with no combat ability, she had to remain in that sealed space.
The existence of that buffer zone was clearly meant to prevent "someone following through the Anywhere Door into the Hall of Path."
For instance, moving too quickly, silently following inside, or the use of invisibility and possibly the launching of some tracker.
Therefore, she had left behind a buffer zone.
