Niddah, Chapter 8, Mishnah 4. This chapter deals with a woman who finds a bloodstain (a kesem) on her garment, and with the circumstances in which such a stain renders her tmeiah as opposed to leaving her tahorah. Our mishnah records an incident that illustrates just how far Chazal were prepared to go in seeking a lenient resolution in these cases.
The incident
The mishnah opens with an actual case: "Ma'aseh be'ishah achas," there was an incident involving a certain woman, "sheba'as lifnei Rebbi Akiva," who presented herself for a ruling from Rebbi Akiva. Her words were: "Amrah lo: ra'isi kesem," she reported to him that a bloodstain had turned up on her clothing.
Rebbi Akiva responded with a question: "Shema makah haysah bach?" Perhaps you had a wound, so that the blood can be assumed to have come from there? "Amrah lo: hen, vechaysah." She answered yes, she had had a wound, but it had already healed over.
Rebbi Akiva pressed further: "Shema yecholah lehigalot ulehotzi dam?" Perhaps the wound is not entirely closed, and it is still capable of reopening and releasing blood? "Amrah lo: hen." She agreed that this was indeed possible, and that such a wound could well be the source of the blood she had found.
"Vetiharah Rebbi Akiva." On that basis Rebbi Akiva declared her tahorah.
The students' astonishment
The mishnah continues: "Ra'ah talmidav," Rebbi Akiva saw his talmidim, "mistaklim zeh bazeh," looking at one another. The glances spoke for themselves: they were startled that so many questions had been put to this woman until a verdict of taharah could be reached.
So he addressed them: "Amar lahem: mah hadavar kasheh be'eineichem?" What is it here that sits so badly with you? And he explained: "Shelo amru chachamim hadavar," the chachamim did not legislate in this area "lehachmir, ela lehakeil," with the aim of adding restrictions, but rather with the aim of relieving them. Hunting for the lenient reading does not undercut what they instituted; it carries it out.
The source in the pasuk
Rebbi Akiva grounded the principle in a pasuk: "shene'emar, ve'ishah ki sihiyeh zavah," and a woman who experiences a discharge, "dam yihiyeh zovah bivsarah," what she discharges shall be blood in her body. The phrasing yields the inference "dam velo kesem": the Torah's tumah attaches to blood as such, not to a mark left on a garment. A kesem, then, owes its status to the Sages rather than to the pasuk.
For that reason, when it comes to bloodstains found on clothing we deliberately search for grounds to be meikil rather than looking for reasons to be stringent. Rebbi Akiva's persistent questioning of that woman was not an unusual stretch; it was the natural way to handle a law whose entire purpose is leniency.