I like reading about dystopian storylines, so I'm wondering if there's a comic that shows how humanity started descending into chaos after the Sentinels became activated.
"Days of Future Past" is a storyline in the Marvel Comics comic book The Uncanny X-Men issues #141-142, published in 1981. This is a divergent timeline from the mainstream Marvel Universe, designated Earth-811
It deals with a dystopian future in which mutants are incarcerated in internment camps. Very few panels of these comics deal with this future state of Marvel Earth. There are later stories which deal with this future but mostly they introduce new characters like Rachel Summers, Nimrod and Ahab, Master of Hounds.
An adult Kate Pryde transfers her mind into her younger self, the present-day Kitty Pryde, who brings the X-Men to prevent a fatal moment in history that triggers anti-mutant hysteria.
Elements of the X-men movie "Days of Future Past" borrow some of the ideas in a rather haphazard fashion. Instead of sending Kitty Pride to the past, the movie sends Wolverine.
The storyline was produced during the franchise's rise to popularity under the writer/artist team of Chris Claremont, John Byrne and Terry Austin. The dark future seen in the story has been revisited numerous times, and was adapted into the 2014 feature film X-Men: Days of Future Past. In 2001, fans voted the first issue of this storyline the 25th greatest Marvel comic.
The Official Handbook to the Marvel Universe: Alternate Universes 2005 gave the numerical designation for the original "Days of Future Past" timeline as Earth-811 in the Marvel Multiverse.
Later, connected or related stories from Earth-811
Of course, preventing Kelly's assassination did not erase this possible future; it only created a new future. Pryde and Summers tried again. Summers traveled back in time. Nimrod, an advanced Sentinel, killed Pryde and followed. Summers visited Professor Xavier's school but quickly left (it had been destroyed by the army in her future, leaving her the only survivor). She joined the X-Men for a time and then became a founder of Excalibur.
A related event, Days of Future Present, took place in the present but involved the Franklin Richards who apparently died in the first story. It also involved a new character, Ahab, who was Master of the Hounds in the future and had made Rachel one of his Hounds.
Another story, actually a prequel, appeared in a limited series, Wolverine: Days of Future Past (December 1997 - February 1998). This story explained, among other things, how Magneto wound up a paraplegic in the first story.
One last story has a similar title but definitely takes place in another reality (Earth-2992). In this story, "Days of Future Tense", the survivors of Excalibur were wiped out by Black Air, a British intelligence agency collaborating with the Sentinels. REF: Earth-811
In this timeline, the dystopia comes about because the Sentinels were tasked with destroying the mutant menace. At one point, the Sentinels, lead by a super sentinel named Master Mold, realized that to eliminate the mutant menace, they would have to start with the source of the problem. Humans. So they attacked humans who could potentially breed mutants, and then all humans. This same back story is given in the 90s X-Men cartoon, and the 2000s Wolverine and the X-Men cartoon. This is the same presented in the DOFP movie. When Wolverine arrives to talk with younger Xavier and Hank:
Past Wolverine: In the beginning the Sentinels were just targeting mutants, then they began to identify the genetics in non-mutants who'd eventually have mutant children or grandchildren. Then they started targeting everybody. Many of the humans tried to help us, it was a slaughter. Leaving only the worst of humanity in charge. I've been in a lot of wars, I've never seen anything like this. And it all starts with her.