לע"נ ר' מרדכי גימפל בן אברהם משה
We are compelled to explain that since the Torah obligates a person to testify, this means that refraining from testifying constitutes active harm. So it would be as if Levi would take a hose to put out the fire in Shimon's house and Ruvein would cut the hose, rendering it useless. So in our case it is as if the plaintiff entrusted the witnesses with the power to help him and they were negligent in their duties.
If our understanding is correct then in a case where a person is not obligated to testify, he would not be responsible to pay. The Kessef Mishna and Minchas Chinuch say that if there is only one witness [until now we have been discussing a case where there are two witnesses] he is NOT sinning if he doesn't testify but is nevertheless חייב בידי שמים to pay. This is a difficult opinion to understand because if there is no sin in not testifying - why should he have to pay? The entire obligation to pay is generated by the obligation to testify which creates a שיעבוד on the witness. If he is a lone witness there is no שיעבוד and thus no חיוב בידי שמים.
עיין בהרחבה בספר אפיתחא דשמעתתא עמ"ס שבועות סי' א