The ONLY purpose of a letter of investigation is to procure evidence from the pilot or other involved party, for the purpose of establishing guilt.
Once one is received, consultation with an attorney is essential, and it's got to be an aviation attorney.
Your question specifically asked if the letter ends badly...the letter is a printed piece of paper and always ends the same.
The outcome of an investigation and enforcement action however, could go any direction. The purpose behind the investigation is a big piece of the puzzle...safety of flight issue, retribution by an inspector, vendetta, making a point, looking for a scapegoat...know the purpose and you'll have a good idea of the outcome.
An attitude of compliance is essential, but many pilots feel the need to confess to everything under the sun in order to grovel and show compliance...and that's not compliance. Talk to an attorney first. The real intent behind the letter is to "offer" the recipient an opportunity to incriminate himself, so make no mistake about where it's going. If a reply is made, great care should be made to admit nothing.
As an example, the FAA receives a report of NXXXX doing low passes over a subdivision. The FAA determines whom they think was flying the airplane, and sends a LOI. The pilot responds by saying he wasn't that low and flew around that area. In his mind, he's refuted the accusation. In reality, what he just did was put himself in the airplane on that day. The FAA didn't know for certain who was in it, and couldn't prove it until the pilot just gave a signed statement it was him. The facts beyond that aren't relevant, because this isn't a trial. The pilot is already convicted...the FAA just needed him to confess to seal up their case.
When FAA enforcement action is taken, it's not done as a guilt vs. innocense thing. It's done as a guilt thing. Unlike criminal court where one is innocent until proven guilty, in the Administrative process, one is guilty until proven innocent. One is violated first (handed the enforcement action), and given the option to appeal later. And...unlike criminal law, if you can't afford an attorney, one won't be provided for you. Nobody needs to read you your rights. And they won't.
Letters of investigation serve to gather evidence to used against you. Meetings face to face are for the same purpose. Consult an attorney before submitting anything in writing, take the attorney with you for the face to face.
When the FAA tables a matter, they often still do an administrative action (penalty) by putting a letter (Warning Letter) in your file for two years. When they can't "get" you they still put this there, often saying something along the lines of "Even though we have no evidence against you, doing XXX is a violation of the regulation," paraphrased. In other words, they don't have a way to get you, but they do it anyway. The good news is that the letter is expunged from the record after two years.
Take even the smallest infractions seriously. The FAA does.