Michael Emerson co-stars as a hospital orderly who's convinced that his patient John, who has an irreversible condition, is special. Emerson is obsessed with mysterious rules, and people suspect he is the Big Bad - but he's not. A crazy amount of action surrounds John's dead body, which turns out not to be so dead after all. But later, it's clear that John died halfway through the series, but he continues as one of the most important characters right to the end. Oh, and Ken Leung is a cop.
Well, that was how the Saw series began anyway. Then came six sequels, some awful, and the low, low reviews overall made the series the single most underrated film saga in history. Also, the single most... plotted original film series in history, horror or otherwise, which would shock anyone who hasn't watched it.
Other than the early cast crossovers, the thing that most closely linked the series with Lost was how much it rewarded close attention and devotion. Continuous, usually logical retcons, Chekhov's guns, minor characters from years ago that suddenly gain importance... all of which is lost on the casual viewer - or reviewer. Of course Emmy judges didn't give a damn about the continuity cavalcade and emotional closure in "The End". And of course critics thought nothing of Saw 3D's amazing final minutes. They instead called the movie "incomprehensible" (along with tons of other, legitimate criticism).
There are other links with Lost too. Non-linear storytelling, in a big way. Ontological mystery. Amazing music. Subjects waking up in a strange place and turning on each other - or working together. Oh, and everyone dies. EVERYONE.
Some people may connect Jigsaw and Ben because of the whole "master manipulator" role and Michael Emerson's part in the series, but I see Jigsaw very much as a Jacobesque figure. He draws people that he sees as flawed and, against their will, subjects them to experiences he thinks will cure them. These experiences almost invariably kill the subjects and do little to support the tester's view of humanity. This video even shows him baptizing his foremost disciple. Both goad their eventually killer into murder, but death is far from the end for them. Their plan continues. They keep communicating with followers. And their successors take up the reins.