Another exception-case that might still fit...
Although technically a part of a franchise (and a terrible, bargain-bin franchise at that,) Spec Ops: The Line was franchise entertainment in name only. In actuality, it was an intrepid assault on the type of games it came from and the gamer compelled to buy games like it. A military shooter on its surface (and in its bloody innards too, right down to its itchy trigger finger,) Spec Ops had an anti-war intent (or at least realities-of-war) loaded into every aspect of the gameplay design and storytelling in the game campaign. It has its flaws and detractions (I actually don't love the game, but I do like talking about it,) but few games are made like Spec Ops: The Line.
...And even fewer, in fact pretty much no games, followed up Spec Ops: The Line from the developer or publisher. Spec Ops itself was a commercial failure and never saw a sequel. Developer Yager Developments never made anything as conceptually out there again, and creative lead Cory Davis eventually went indie. (He currently runs a studio called Eyes Out, with NIN guitarist Robin Finck.) And although 2K Games was in bull mode to continue putting its money where its mouth was in backing creatives with bold concepts like BioShock and the Rockstar releases, eventually that enthusiasm settled on more conventional ways of making money. (We'll see how wild Judas is when it finally is finished...) Spec Ops The Line didn't need a sequel (and some might say it didn't deserve one), but it's a singular experience remembered well by its supporters and buried well by its studio.