Let's say someone found $2,000, but as a trail it lead to a dead person. The police obviously need it. But after they're done with the case, do the founders get to keep it?
In the UK you may be able to keep it.
Q: If I've found someone else's property can I keep it?
A: You may be able to keep hold of the item you have found on the understanding that if the owner comes forward, you must give it back. If the item is retained by the police and the owner is not identified within 28 days you are entitled to claim it back. There are certain items that members of the public are not allowed to retain and claim under any circumstances. These include mobile phones, identification documents, weapons and war medals. If you find cash, you will not be able to keep hold of it, but will be able to claim it after 28 days.
However if the owner is identified but dead then, as @SJuan76 says in the comments, the money goes to the estate of the deceased.
In most places, since "a trail lead to a dead person" you most likely have fulfilled your duties to find the rightful owner, and in most places if the rightful owner cannot be found, you would keep it.
You would have to check exactly what laws apply. Different jurisdictions usually have roughly the same goals with their laws, so in the usually lost+found property case, the legal outcome would likely be the same, even if the laws are slightly different. Your case me be unusual and not something that the law makers though about when they wrote the law, so in an unusual case there could be different legal outcomes, depending on the exact wording.