Totally by accident I've just happened to run across the 2014 open access paper A peculiar stable region around Pluto with the abstract below.
The purpose of the paper was to see if stuff might already be in some long-lived orbits around the system, things that New Horizons might pass near and photograph, or perhaps even collide with.
I don't know if New Horizons looked or not, but if you wanted to put something there in the system that would remain stable for a while, this three-body orbit will last quite a while.
and included from that paper
[...]The relevance of the sailboat region for the New Horizons spacecraft is addressed in Giuliatti Winter et al. (2014). In this work, we verified that the nominal trajectory of the New Horizons passes near the region of the sailboat region trajectories and we also identified the location of the densest regions, which corresponds to the highest probable location of particles of the sailboat region.
and the image below.
Question: Did New Horizons pass through or nearby this "sailboat region"? Did it spend any time looking for small objects that may have collected in it, or trying to avoid hitting any of them? Did it pass through this region or did it stay way from it during its flyby?
The set of periodic orbits, in the synodic frame, for different values of CJ presented in Fig. 2. The barycentre is located at 0, the origin of the coordinate system. The large and small black dots indicate the location of Pluto and Charon, respectively.
Figure 7. A sample of periodic (in black) and quasi-periodic (in yellow) orbits, in the synodic frame, for (a) CJ = 2.786 and 2.936, (b) CJ = 3.016 and 3.056, and (c) CJ = 3.116 and 3.224. Pluto is represented at the position (−0.1, 0) and Charon at (0.8, 0). The quasi-periodic orbits presented here are those with the largest amplitude of oscillation which correspond to the largest islands in the Poincaré surface of section (Fig. 2).