Since when do we believe anyone who claims something as theirs? Perhaps the woman wants the Get to claim her Kesubah or to marry another man? The fact that she is believed to say that her husband died in order to remarry is a special dispensation to spare a woman from becoming an Agunah (who can never marry), as the Gemara discusses in Yevamos, And that dispensation is based on the Chazakah that the woman will not remarry before having made extensive enquiries to ascertain that her husband is in fact dead. And that Chazakah is reinforced by the fact that, well aware of the dire consequences that she will face should he return, she will not dare remarry unless she is a hundred per cent certain that he is no longer alive.

Wishing you and your family a Kesivah va'Chasimah Tovah

Eliezer Chrysler.