Commentary for Genesis 4:15

לכן כל הרג קין VERILY, WHOSOEVER SLAYETH CAIN — This is one of the verses where the construction is elliptical (literally, which abbreviate their statements), which give only a suggestion and do not fully explain. “Verily, whosoever slayeth Cain” express a threat, suggesting the consequence — “thus shall be done to him”, “thus and thus shall be his punishment”, without explicitly explaining what the punishment would be.

Now because Scripture says, And the Eternal appointed a sign for Cain,⁴⁴⁴Verse 15. and it does not say, “and G-d gave him a sign,” or “made him a sign,” it indicates that He appointed for him a steady sign which would always be with him. Perhaps it indicates that as he wandered from place to place he had a sign from G-d indicating the way in which he should walk, and by that he knew that no misfortune would overtake him on that road.
In Bereshith Rabbah⁴⁴⁵22:27. the Rabbis similarly stated, “Rabbi Aba said: ‘He gave him a dog.’” Since he feared the beasts, He gave him one of them to walk before him, and wherever the dog turned to go, Cain knew that G-d commanded him to go there and that he would not be killed by any living creature. Now the Sages singled out a contemptible sign [a dog] as was befitting him, but the intent is that there was with him a perpetual sign showing him the way to go for such is indicated in the word vayasem (and He appointed).

כל הורג קין שבעתים יוקם, I, G’d, announce that anyone who dares to kill Kayin, [i.e. who takes the law into his own hands, Ed.] would be punished seven more times than what the crime he committed appears to warrant. Anyone who is prepared to kill someone is called הורג, as for instance, in Hoseah 9,13 ואפרים להוציא אל הורג בניו, “Ephrayim too must bring out his children to his slayers.” The word שבעתים means “twice seven times,” as in Proverbs 6,31 ונמצא ישלם שבעתים, “when he is found out he must pay twice sevenfold.” G’d decreed therefore that when someone killed half the human race, or at least a third of the human race, the appropriate vengeance would involve a twice sevenfold penalty. This would manifest itself in such a slayer being a restless wanderer on earth for seven generations. Such a life is considered worse than death. When David prays in Psalms 59,12אל תהרגם פן ישכחו עמי הניעמו בחילך, “do not kill them lest my people will forget them; make them wanderers seeing it is in Your power,” he meant that they be killed only at the end of seven generations. David wanted the punishment of his enemies to last. If they would all die and disappear at once their absence would soon be forgotten. Kayin got his deserts at the end of seven generations as we know from traditional sources in Tanchuma 10.