In some cases the negative or "relaxed" stability of the aircraft is a consequence of the design, rather than an explicit design goal. I'm thinking here of the F-117 and the B-2, whose fuselages are very unorthodox due to stealth requirements. Aircraft such as these require FBW systems to stay aloft.
In fact I once heard the B-2 described as being "held in the air by sheer computing power"
Other aircraft such as the F-16 are designed to be intentionally unstable.
People often get mixed up due to the terms stable/unstable having very specific, prescribed meanings.