I want to address the area of unsolved homicides.

It is important to not interfer with the active investigation of law enforcement but also it is very important not to let the case grow very cold if you can help it.  I was called to investigate one case of a high profile local citizen who was murdered in his home. I made the mistake of not taking the case early on because I wanted to give the local law enforcement a chance to investigate.  As a result valuable evidence was lost, the crime scene was compromised and the case grew colder until the next time I was contacted.    

Family members and friends often know if they need outside help depending on their confidence in local law enforcement.   If the law enforcement has overlooked evidence later found by the family or allowed a crime scene to be compromised or just are not doing a thorough job it is important for the family to act as quickly as possible. Unfortunately at times local police or deputies are uncertified, not properly trained or interested in getting to the truth for a variety of reasons.  This is very unfortunate but true.  The suspect could be a confidential informant, a relative of someone of influence in the community, or  the victim may not be important enough to the community [although obviously very important to the family] for the local law enforcement agency to spend time, money and resources on the case.

A private investigator does not have these limitations or motivations as his or her job is to get to the truth and to uncover every hidden thing, digging and asking questions at every turn.  

It is not impossible to work a case that has grown very cold and sometimes there could be some advantages as some people are more apt to to respond to questions when they feel that time and danger has passed.

Recollections are obviously not as accurate in detail with some people needing to be interviewed but then you may have more people available to corrobate details.