Does divorce or khul' take effect by signature alone, without documenting the verbally agreed-upon compensation, due to the wife's lack of sufficient funds to pay the agreed-upon compensation?

Khul' is valid with the husband's offer and the wife's acceptance, whether it is written or not. It has explicit wordings that do not require intention, such as: "I divorce you [through khul']", or "I annul your marriage", or "I ransom you." There are also implicit wordings such as: "I absolve you [from the marriage bond]", "I release you [from the marriage bond]", "I separate from you." Khul' does not depend on a judge's ruling. If the khul' is completed with a known compensation, it becomes valid and the woman becomes irrevocably separated. The compensation becomes a debt upon her if she does not deliver it to the husband.