A debt which is written in the תורה, etc. - מלוה הכתובה בתורה
מלוה הכתובה בתורה is when the תורה teaches us that there is an obligation and how this obligation is to be discharged. A loan is not a מלוה הכתובה בתורה, since it is obvious how the obligation must be discharged.
How de we derive, however; the death of the husband - אלא מיתת בעל מנא לן
After the תורה teachers us by א"א that death dissolves any איסור which was caused by marriage, it is necessary for the תורה to teach us that by certain עריות (caused by marriage), the איסור continues even after the marriage ceases.