Taharos, Chapter 4, Mishnah 2. This chapter is devoted to the many varieties of safek tumah, cases where we simply cannot determine whether an object became tamei or remained tahor. Our mishnah belongs to a run of cases built on one idea: tumah that is in motion. When the source of tumah never comes to rest, even a genuine doubt, and even a doubt that arose in a reshus hayachid (a private domain, where doubts are normally ruled tamei), is resolved leniently. Tumah on the move slips past the rules of safek and leaves everything tahor.
Here is the situation the mishnah describes: "hasheretz befi hachuldah umehaleches al gabei kikaros shel terumah" - a chuldah (a weasel) is holding a sheretz between its teeth, and it is scampering across a row of terumah loaves. A sheretz is one of the eight small creeping animals whose carcass transmits a severe grade of tumah. Terumah is exactly the food for which such a scene raises alarm, since it has to be kept in a state of taharah and may no longer be eaten once tumah reaches it. So we have an animal with a source of tumah in its jaws passing over these loaves, and no way to establish what actually occurred.
"Safek naga safek lo naga" - perhaps contact was made and perhaps it was not. We do not know whether the weasel actually brought the sheretz into contact with any of these loaves. And the ruling is "sfeiko tahor": the doubt is decided in favor of purity. The reason is the one that governs this whole series of cases: the weasel is in constant motion. The tumah it carries has no fixed place, no settled location where it can be said to reside, and therefore the doubt about it does not carry the weight that would render the loaves tamei.
The mishnah then pushes the case further. This ruling holds not only where the loaves are lying on the ground by themselves, but even where a person is holding them. That distinction matters, because in the laws of safek tumah a great deal turns on whether there is someone present who yesh bo da'as lehisha'el, someone with the awareness to be questioned about what happened. Ordinarily, the presence of such a person is what allows a doubt to be ruled tamei; where no one can be asked, the halachah is lenient. Here, however, that entire consideration is set aside. Even with a human being involved, even one who could be interrogated about the incident, the loaves remain tahor, because the decisive factor is that the weasel, and with it the sheretz, never stopped moving.
The lesson of this mishnah, then, is that motion itself is what disqualifies the doubt. Tumah being carried along in the mouth of a moving animal has no resting place, and without a place, the safek cannot take hold.