In Shariah, Kafalah (surety/guarantee) comes into existence by the proposal from the guarantor and the approval from the creditor’s side. Therefore, if it was done without the approval of the creditor, it will not be applicable; rather, it would be treated like a promise.
Additionally, guarantee/surety can take place by the order of the debtor or without his order. Thereafter, if the guarantee/surety was formed in result of a request or order from the debtor, the guarantor will have a right to claim back whatever he paid and if it was without the order or request, then it was a favour from the guarantor which he cannot claim back.
Furthermore, if the creditor agreed and approved the idea of the guarantor paying on behalf of the debtor, the creditor can demand the money from the debtor or the guarantor; however, if the creditor did not approve of the idea or was unaware of the settlement, the guarantor will not be obliged to pay; rather, it would be an act of goodness and favour.
In the light of the above, we proceed to your enquired query:
If the third-party acknowledged the surety, they are permitted to demand from the debtor or the guarantor. If the debtor does not settle the debts, the guarantors will be liable to pay with the proviso that the surety took place with the approval of the creditor.
If the guarantors gave guarantee together, each will be liable for his portion. For example, if they were four guarantors, they will be liable for a quarter of the amount each. If they stood guarantee individually, not in the presence of each other, each will be liable for the full amount. The creditor can decide who he wants to take it up with. Once he gets his money from the guarantor he targeted, the others are absolved. [Al Majallah article: 647]
The guarantors need to ponder and confirm how many people stood as a guarantor in the enquired case; otherwise, the issue will be solved by a judicial process in arbitration. Lastly, paperwork is not necessary in order to become a guarantor.