The static friction and the kinetic / dynamic friction are two different phenomena. The coefficient of static friction is always greater than that of the dynamic friction. Therefore, the limit of small sliding velocity (V→0) is different from the case of zero velocity (V=0). In physics, such situation is called a “singular limit” (see, for example, excellent popular papers by Michael Berry and by Leo Kadanoff).
While the onset of friction (the transition from the static to kinetic friction) is being studied in detail, the opposite transition (from the motion to the rest) is of interest as well. It is clear that the inherent deformability of a sample is an artifact that cannot be eliminated during the study of very slow friction.
I hope that using a CETR / Brukner tribometer in my lab, along with collaboration with Dr. Alexander Breki, the Head of the Friction and Lubrication Lab in St. Petersburg Polytechnic University, who designed a novel instrument to measure ultra-slow friction, we will be able to shed more light upon this scientific problem.
As always, we are interested in funding. Currently we have no funding for this research, so if you know somebody willing to support this amazing research area, please let me know.