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We all know that after Kayin kills his brother and finds himself confronted by God, he says to God, גדול עווני מנשוא - "my sin is too great to bear" (Bereishit 4:13). Yet, it's not altogether clear whether in this cryptic statement Kayin fesses up to his heinous act and his statement represents a declaration of repentance, or whether he rejects God's wrath telling Him, "Sorry, it's all too much for me to worry about, God. Not my problem." (I think it's the latter, but it's a huge machloket.) In any case, God responds that, "Whoever kills Kayin will be punished seven-fold," (verse 15) and God gives a "sign" to Kayin to protect him. What sign did God give Kayin. The Midrash says,
אמר ר' יהודה - הזריח לו גלגל החמה. א"ר נחמיה - לאותו רשע היה מזריח לו הקב"ה גלגל החמה? אלא מלמד שהזריח לו הצרעת...רב אמר כלב מסר לו. אבא יוסי בן קסרי אמר קרן הצמיח לו. רב אמר עשאו אות לרצחנים. רבי חנין אמר עשאו אות לבעלי תשובה - בראשית רבה כ"בRabbi Yehudah said, [God] rose the sun for him. Rabbi Nechemia said, For that evil person would God have risen the sun? Rather, it must mean that God shone upon him leprosy. Rav said that he gave him a dog. Abba Yossi ben Kisma said that he grew a horn upon him. [Another] Rav said that he made him a sign for murderers. Rabbi Chanin said that he made him a sign for Ba'alei Teshuvah. (Bereishit Rabbah 22)
Clearly, the rabbis in the Midrash themselves couldn't agree whether Kayin had repented, and interpreted the sign that God gave Kayin in light of how they viewed his declaration. If they felt that he did repent, he got the sunrise or a "sign for Ba'alei Teshuvah" (whatever that was). If not, he got leprosy, or a horn. (Was he then the first "humacorn?" Get it: human + unicorn?)
In any case, what about the dog? Was it a sign of his repentance, or of his refusal to repent? Rabbi Hoffman notes that Ramban, who quotes the Midrash, sees the dog as a sign of Kayin's repentance, as the dog would now serve to guide him away from any dangerous animals looking to kill him.
I've got my doubts. Despite our current infatuation with dogs as pets, Chazal (as well as the Torah) didn't see dogs in a very positive light. Think of the dog references in the Torah. What do we do with treif meat? We "Throw it to the dog." When is chametz no longer forbidden? When it's no longer ra'ui l'achilat kelev - "edible by a dog", the lowest of animals.
I guess then if you're a dog owner, you'd have to agree with Ramban and see the dog as a gift. But if you're not, Kayin's dog might be more of a punishment than a gift.