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The act you are describing is extremely unethical. 
First off, I want to point out that comparing human beings to stray dogs is disturbing to say the least, and is not the mark of an unbiased point of view. More importantly though - this is someone who possibly views you as a friend, and you are about to turn them in to a massive mindless bureaucracy whose goals are predicated on flimsy or even repugnant ethical grounds. Unless this person is a known criminal, or you know they are going to inflict certain harm on other persons by staying in your country, then you are only going to do harm and not good by turning them in.
EDIT: I don't think my answer is clear enough. The original question looks like it was edited to remove a comparison of reporting illegal immigrants to the INS with reporting stray dogs to animal control. That analogy fails, because human beings are not dogs and they have rights that dogs don't have.
I think also I should clarify that I'm dispensing right away with the notion that obeying the law of the land is equivalent to doing the moral thing, because there are so many counter examples. Therefore, turning in illegal immigrants has to be defended morally on its own merits aside from legal considerations.
And what are the merits of turning over someone to the INS? Does it help them? No. Does it help you? No. So who does it help? If you can't name any party that is helped, but you can easily name a party who is harmed (the immigrants, the community they are a part of) then the moral thing is to let them stay.

The act you are describing is extremely unethical. First off, I want to point out that comparing human beings to stray dogs is disturbing to say the least, and is not the mark of an unbiased point of view. More importantly though - this is someone who possibly views you as a friend, and you are about to turn them in to a massive mindless bureaucracy whose goals are predicated on flimsy or even repugnant ethical grounds. Unless this person is a known criminal, or you know they are going to inflict certain harm on other persons by staying in your country, then you are only going to do harm and not good by turning them in.

The act you are describing is extremely unethical. 
First off, I want to point out that comparing human beings to stray dogs is disturbing to say the least, and is not the mark of an unbiased point of view. More importantly though - this is someone who possibly views you as a friend, and you are about to turn them in to a massive mindless bureaucracy whose goals are predicated on flimsy or even repugnant ethical grounds. Unless this person is a known criminal, or you know they are going to inflict certain harm on other persons by staying in your country, then you are only going to do harm and not good by turning them in.
EDIT: I don't think my answer is clear enough. The original question looks like it was edited to remove a comparison of reporting illegal immigrants to the INS with reporting stray dogs to animal control. That analogy fails, because human beings are not dogs and they have rights that dogs don't have.
I think also I should clarify that I'm dispensing right away with the notion that obeying the law of the land is equivalent to doing the moral thing, because there are so many counter examples. Therefore, turning in illegal immigrants has to be defended morally on its own merits aside from legal considerations.
And what are the merits of turning over someone to the INS? Does it help them? No. Does it help you? No. So who does it help? If you can't name any party that is helped, but you can easily name a party who is harmed (the immigrants, the community they are a part of) then the moral thing is to let them stay.

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The act you are describing is extremely unethical. First off, I want to point out that comparing human beings to stray dogs is disturbing to say the least, and is not the mark of an unbiased point of view. More importantly though - this is someone who possibly views you as a friend, and you are about to turn them in to a massive mindless bureaucracy whose goals are predicated on flimsy or even repugnant ethical grounds. Unless this person is a known criminal, or you know they are going to inflict certain harm on other persons by staying in your country, then you are only going to do harm and not good by turning them in.