Person of Interest” aired what could be its final episode Tuesday – the program’s renewal prospects remain uncertain heading into CBS’ fall upfront presentation – and in some respects, the series offers a cautionary tale. Not just about artificial intelligence and the surveillance state, which provided the show’s cerebral foundation, but also the challenges in allowing what at its heart was initially a crime procedural, on a network overflowing with them, to morph into a more serialized drama, until the program practically choked on its own dense mythology.

Conceived largely as a two-character piece – Batman’s billions and brains (Michael Emerson) and brawn (Jim Caviezel) split into two guys – the series drew depth and strength from its expanded roster of players, including the since-departed Taraji P. Henson and Kevin Chapman as two cops who gradually joined the operation. Then there was the cold-hearted mercenary Shaw (Sarah Shahi) and the villain-turned-uncomfortable-teammate Root (Amy Acker), whose ongoing flirtation with Shaw became one of the show’s more amusing elements.

The finale, however (and SPOILER ALERT if you haven’t watched), felt particularly messy, even if it did manage to extract genuine emotion from the plight of The Machine. That would be the elaborate system created by Emerson’s Finch, which actually “spoke” to its creator as it faced obliteration at the hands of Samaritan, a rival A.I. construct being used by a shadowy cabal with far more nefarious ends in mind.

This season, in fact, essentially blew up the central conceit about Finch and Reese (Caviezel) using The Machine’s cryptic warnings to help those in need, inasmuch as they spent much of their time on the run, trying to stay off the grid to avoid Samaritan’s reach. That culminated in a protracted hostage situation and shootout, with the outnumbered Reese, Root and Finch salvaging what they could of the Machine’s memory and wading into an army of thugs, guns blazing. (For some reason, the last shot in “Angel” came to mind.)

Amid the action, the show also appeared to sacrifice one of its more intriguing recurring characters, Enrico Colantoni’s Elias, as Samaritan’s henchman proceeded to eliminate all threats.

Clearly, there was no definitive closure here. And if that’s all she wrote (or programmed), those fans who would like to see the series return – who made their voices heard in USA Today’s annual “Save our show” survey – will have good reason to howl for more. Sure, shows get canceled all the time, but ending in mid-cliffhanger is poor customer service.

To their credit, the show’s creative brain trust, led by Jonathan Nolan, didn’t play it safe, which, despite its vigilante-style law-and-order element, has made the series a somewhat awkward fit with CBS’ alphabet soup of “NCIS” and “CSI.” The show also features a welcome sense of playfulness and humor, while filling in details like Finch’s backstory that have enriched the characters.

Still, CBS has kept churning out a certain kind of crime drama for a reason, and those who stray too far beyond those parameters do so at their peril. “Person of Interest” deserves some kind of wrap-up, and a shrewd network might dial up a truncated order – to be used as a midseason replacement when something inevitably fails – to do just that. Either way, a series that started with considerable promise ultimately wrote itself into corners from which there was no easy exit — running afoul of TV’s rather unforgiving machinery.