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if you killed them. there's evidence. people have already answered your question.

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lets imagine that it occurs in a place where you have been occasionally, therefore hair, fibers, etc have an excuse for being there. the murder occurs with the victims weapon. the victim is a young, black low profile drug dealer with a small record- not exactly a high priority for most major cities' police departments.

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I'm not trying to nitpick but the list of parameters you keep coming back to to establish that there is no evidence is still flawed. Just because a small-time punk gets killed, you cannot say the police will not consider it a priority because they will want to see if they can tie the murder to a bigger fish...this is how it works.

That being said, I understand this is not what interests you but what my point is it may go inactive within days/weeks/years but it could become active again at the drop of a hat.

Given your new example of there is an excuse for trace evidence of you to be there you and you are eliminated as a suspect, you could be still re-considered a suspect at any time.

As an example of this, I have worked at least 2 non-murder cases that led to people who had been considered suspects in murder cases causing them to be re-examined by the original investigating department and then subsequently indicted/convicted for the original murder cases.

In the end, again, there are no absolutes here. The perpetrator may walk and never be touched again after only a few days if investigation or could be picked up 30 years later. There is no (and shouldn't be) any sigh of relief!