Chazal explain that the process of eglah arufah was an opportunity for the leaders of the city and judges to confess that they did no wrong. Of course we do not suspect the leaders of actually having committed murder. But who would likely fall prey to a murderer other than a lonely soul, perhaps someone passing through town, someone who had no friends or protectors close by? The city leaders are responsible for seeing that wayfarers have food and lodging; they thereofre had to declare that their city was not hostile to strangers, that a guest would find a welcoming home to stay in and accompaniment on his journey when he chose to leave.
R’ Yehudah Leib Chasman asks: if this is the reason for the eglah arufah ceremony, wouldn’t it make at least as much sense to perform the ceremony after the murderer was found as beforehand? Let’s say the victim was in fact a traveler killed by a bandit -- wouldn’t there be even more reason to offer an eglah arufah and confess that the traveler was not ignored, that he was made welcome, after knowing that these were the facts? Yet, the halacha is that once the murderer is known (even if there is but one witness), the eglah arufah ceremony is not performed. Why?
He answers with a yesod that the ba’alei mussar speak of in many places. Once the facts of the case are known, it is obvious to all that amends need to be made. The leaders don’t need an eglah arufah to point a finger at them and remind them that they are the parties responsible to see that strangers are made welcome in their town. It’s only beforehand, when the facts are unclear, that there is the tendency to dismiss events as random occurrences rather than as symptomatic of any wrong. Human nature is to sweep the problem under the rug so long as it is possible to do so. Therefore, precisely in those circumstances, the Torah demands an eglah arufah as a reminder that an accounting is necessary.