How is Kiddushin brought about through money? When a man gives a woman money or items worth money and says, "Behold, you are betrothed to me - Harei at mekudeshet li," and she agrees, she is betrothed.
Anyone who does not know the laws of divorce documents and Kiddushin should have no dealings with them, for an unwitting error in the decision could prove intractable.
A woman can not be betrothed by forgoing the repayment of a loan. The loan is given for expenses, with the obligation to repay. Thus, he is not giving her anything of value at this moment.
How about a document? A document is drafted by a man, and it states that a woman is hereby betrothed to him. The Kiddushin is effected when the man gives the document to the woman.
Why does this work? Because “And she will leave the first husband's house, and she will go and be a wife unto another man.” Since “leave” can be effected through a document, so too “be” can be effected through a document.
But if so, can divorce be effected by money? - No, because a defender cannot become an accuser. And while the documents would be different and distinct, money would be the same.
Art: A Young Lady and a Cavalier by Frans Francken (III)