The pairing with Parashah Chayei Sarah, whose name means the life of Sarah even though it opens with her death, rests on a shared structure rather than a shared vocabulary: both accounts concern an aged figure, Abraham in the parashah and David in the haftarah, arranging for the next generation's security while still able to act, rather than leaving the matter to chance after death.
Abraham secures Isaac's line by sending his servant to find Rebecca rather than allowing his son to marry among the local Canaanite population, an active, deliberate intervention in his own household's future. David, similarly weakened by age, still finds the strength to act decisively once alerted to Adonijah's premature claim, confirming Solomon as his successor before his own death rather than allowing the succession to be settled by whoever moved fastest.
Both narratives also share a secondary figure entrusted with carrying out the patriarch's wishes, Abraham's unnamed servant and Nathan the prophet respectively, each acting as the instrument through which an aging leader's intention is actually carried into effect at a moment when the leader himself can no longer manage every detail personally.
Both accounts also share a moment of hesitation overcome: Abraham's servant prays for a clear sign before approaching Rebecca at the well, and Bathsheba and Nathan wait until the situation is genuinely urgent before finally approaching David directly, each account showing that even a decisive intervention on a patriarch's behalf is undertaken carefully rather than rushed into without reflection.