Rav Yizchok Zilberstein (Aleinu L'Shabeach Vayikra page 317) describes a strange case. A woman is being beaten by her husband. She goes and complains to beis din. They simply tell the husband to behave himself - but the beatings go on. There were no witnesses for her claims - which is common in such cases. Her brothers, seeing nothing was being done - hired two people to be false witnesses on her behalf and to testify that they saw the husband beating her. The beis din carefully examined the false witnesses and decided that they are telling the truth. Based on this testimony the beis din orders the husband to give his wife a divorce - which is the law in Shulchan Aruch.
After she received the Get she went to Rav Silberstein to ask whether she can remarry with a Get given because of false witnesses - who were telling the truth about her beating. She said, "It is clear that what the witnesses said was true that the husband beat me. But on the other hand they lied when they said that they witnessed it. Is the Get posul?"
Rav Silberstein felt that the Get was valid because we accept the principle that every Jew wants to do what is right in the eyes of G-d. The reason why we sometimes force the husband to give a Get is because his yetzer harah sometimes prevents him from doing the right thing. In this case the husband is well aware of the truth that he was beating his wife. In his heart he knows that he has an obligation to divorce his wife. Therefore we can consider that he gave the Get willingly - even though he was forced to give it.
However Rav Eliashiv did not agree with this reasoning and stated that it is prohibited to remarry with a Get obtained through false witnesses. However in this case since the woman already has the Get there is no reason to tell the husband that Rav Eliashiv said the Get is not valid....It is possible to say to him that since the Get already is in the hands of his wife perhaps he will now write a get of his own free will...