i would never, ever, let one of my students pass just because of they start crying, no matter how much i like them personally. nor would i give someone a better grade just because i like them or feel sorry for them.
a test is there to measure someones ability or knowledge on a certain field and if someone does not have this ability or knowledge it would be nothing but cheating to let them pass, and extremely unfair towards the other students.
i would talk to the person crying to see what the problem is. when someone isnt well prepared or has some kind of blackout i would offer to help the person prepare for next time. in case it is a final test because the person has screwed up the test twice before or something i would advice the person to see a doctor immediately so that this test can not be counted as fail and also offer my help for the final test.
when i am convinced they are actually good but just freaking out because they are really nervous, i would try to calm them down and tell them that they know this.
the only exeption i can think of would apply if i had some other measurement for that persons ability or the person has proven his/her knowledge to me numerous times before and it is absolutely clear that they have a different problem.
if someone has some personal issues at the moment for example or is suffering from severe anxiety related to the test, i would let the person pass based on an oral exam some time later, or, if it already is an oral exam and talking is the problem, a written exam, or whatever helps. the way someone shows his/her ability does not matter to me, it only matters that they do.
ignoring students who are crying or even being mean to them or letting them pass regardless of what they can just because they are crying are behaviours i find shocking and can not understand.
i have always reacted in the manner i described above and i do not know if some people would see this as "heartless" but i think that i am fair.