Hi there and thank you for your question,
I will try to assist you with your legal question but please feel free to ask as many follow up questions as you like until you are 100% satisfied.
Q: Can X institute proceedings against A and B jointly for the outstanding amount. --> No, X can not institute proceedings against A and B jointly for the outstanding amount. The reason for this is that the original loan agreement was between A and X. Party B was never a party to the original agreement. Party B only assisted Party A in paying back some of the money - which does not mean that Party B now "becomes" a party to the agreement.
Party B's defence is that she was never a party to the original loan agreement and according can't be sued for repayment of a third parties debts. That is an excellent defence which would stand up in court.
It makes NO difference that the helped Party A repay some money to X.
IF however Party B signed a suretyship, then my answer would be completely different!
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Good luck and best regards,