The ultimate judgment against a wicked person reaches its absolute peak with a demand for total annihilation. This destruction is not limited to his own life but seeks to erase his family and his historical memory entirely [מלבי״ם]. The target of this devastation is his future, understood by most commentators as his children and descendants [רד״ק, אבן עזרא, מצודת ציון, מלבי״ם, מאירי], while others expand this to include his entire legacy [ביאור שטיינזלץ]. The desire is for his offspring to be completely cut off and killed, leaving absolutely no trace behind [רד״ק, ביאור שטיינזלץ], with some suggesting they will perish from starvation [אלשיך].
This complete extinction is destined to unfold in a subsequent generation, though commentators offer different views on exactly when this will happen. It may occur during the lifetime of the sons themselves [מאירי]. Alternatively, the destruction might wait until the third generation [רד״ק, מצודת דוד], or it simply refers to the new people who will populate the world only after the wicked man and his family have been entirely wiped out [רש״י]. The curse intentionally broadens its scope to ensure that the erasure applies equally to both the father and his son [רד״ק, אבן עזרא, מצודת דוד, מאירי], or to the father and all of his descendants combined [ביאור שטיינזלץ].
The final result of this curse is a complete uprooting from human consciousness. The wicked person's identity and character will be wiped away so thoroughly that future generations will never even speak his name, and he will be completely forgotten from the hearts of men [רש״י, מצודת דוד]. Ultimately, the only surviving trace of this person will be the memory of his sins and crimes against God, which will serve as the sole explanation for why his family was destroyed [מלבי״ם, ביאור שטיינזלץ].