When realization expenses are paid by the firm on behalf of a partner (who was explicitly given the responsibility to bear them), which account must be debited in the firm's books?

If a partner is assigned to bear the realization expenses, it becomes their personal liability. If the firm pays these expenses on their behalf, it means the firm is paying out cash for that partner's personal obligation. This reduces the partner's equity in the firm.The entry passed is:
$$\text{Partner’s Capital A/c}\text{Dr.}$$
$$\text{To Bank/Cash A/c}$$
Thus, the Partner's Capital Account is debited.