Facing the inevitable reality that the kingship will soon pass to his rival, a desperate king seeks to secure his legacy. Fully grasping that his royal line is coming to an end, Saul demands an oath from David to guarantee the survival of his family, echoing a similar promise his son Jonathan had secured earlier [ביאור שטיינזלץ].
Saul's plea focuses on preventing the absolute annihilation of his family line [מצודת ציון]. His demand carries a severe warning: if the agreement is broken, the heavy punishment of a violated oath will fall upon the transgressor [מצודת דוד]. The primary approach among commentators is that his dual plea to spare his offspring and protect his name does not represent two separate requests, but rather a repetition meant to emphasize the depth of his concern. Eradicating a person's children inevitably destroys their name, as it is through descendants that a legacy is preserved and remembered across generations [רד״ק, מצודת דוד].
David readily accepts this solemn promise. His willingness to swear to his pursuer stems from a clear certainty that he will indeed ascend to the throne, coupled with complete trust in God and a reliance on his own good deeds to guide his future path [אברבנאל].
This sworn agreement raises a historical question regarding later events, when some of Saul's descendants were handed over to the Gibeonites. Despite this outcome, the promise remained intact. The oath was not violated because David did not execute the descendants with his own hands; rather, the Gibeonites were the ones who actively carried out the deed [מלבי״ם].