This is considered a radical solution: when obtaining the get is problematic, the Rabbinic Court would annul the marriage retroactively.
How can this be possible according to Jewish Law?
Betrothal annulment is mentioned in a few places in the Talmud, and is based on the principle by which "anyone who betroths a woman does so in accordance with the Sages". This is also the reason why in the marriage ceremony the man tells his wife "you are hereby betrothed unto me by means of this ring according to the laws of Moses and Israel". How does this relate to the issue before us? Since the marriage was performed according to rabbinic authority, they can also annul it on the basis of their own authority.
The cases mentioned in the Talmud are specific cases; for example: the husband betrothed his wife against her will or decided to give her a get and then changed his mind. Nowadays, there is a debate on two questions:
(1)When can a betrothal be annulled?
(2)Do the rabbis have the authority to annul marriages in post-Talmudic times?
An example to such a debate can be seen in a case that occurred in Germany in the beginning of the 12th century. A young woman from the city of Cologne agreed to marry a certain young man, changed her mind and chose to marry someone else. While standing under the huppah, before the ceremony, the relatives of the first man arrived with the intention of saving his honor. Before she understood what was happening, they threw an object at her and said in the presence of the witnesses "you are hereby betrothed unto So and So". The bride’s parents, who immediately understood what had happened, called out to her to “throw the betrothal [the object that sealed the betrothal transaction] from your hands!!!” She did as they indicated.
Following this case the following question came up: was her marriage to the first young man, which was carried out by his family in a fraudulent fashion, valid or not? The answer- it appears- is not simple.
In this case, the scholars from Worms and Speyer attempted to annul the first betrothal without a get based on the Talmud, due to the improper nature of the betrothal. The Magenza scholars claimed, on the other hand, that the scholars from Worms and Speyer did not have the authority to annul the marriage as was done in Talmudic times. In the end, the young woman's father was forced to bribe the first man so that he would give his daughter a get. Only after the get was given, was she able to marry the second man.
For hundreds of years marriages were annulled in few and exceptional cases. These were mostly cases involving fraudulent or dubious betrothals, or cases in which it was necessary to resolve a difficult situation such as one involving mamzerim [bastards according to Jewish law]. Betrothal annulment was done through local enactments (local Rabbis took the authority upon themselves to annul betrothals).
This solution is not a routine one for solving the problem of Agunot and women who are refused a get. The Rabbinic Court of the Conservative movement in the U.S. uses betrothal annulment as a legitimate solution to the problem (in a limited fashion, when it is impossible to obtain a get). It is important to state that this solution is not accepted by Orthodoxy which claims that betrothal annulment was indeed used in special and rare cases, however; it cannot be employed as a standard solution. This solution came to the forefront in the past several years in the State of Israel: Rabbi Shlomo Riskin suggested applying betrothal annulment on the basis of an enactment by the Chief Rabbinate in which it would to take such authority upon itself and Professor Berachyahu Lipshitz suggested that the Knesset should allow betrothal annulment on the basis of a law that would function as a community enactment.