I'm distraught about Clifton but I'm going to talk about him anyway

 Tod Clifton is an enigma of a character in Invisible Man, but it's hard to figure out why at first glance. You can tell there's something important about him, but you're not quite sure what. His entrance into the story feels like it's filled some sort of void (or perhaps I'm projecting my grief onto you), and his exit is bittersweet and leaves multiple characters angry and confused.

Before we can answer the Tod Clifton question, we must talk about the narrator. Throughout the entire book, there is one specific thing that the narrator never really gets: a friend. He's had a temporary caregiver in Mary, but he was bothered by her preaching and looked down on her for having racist memorabilia in her house. He had a kind of paternal figure in Brother Tarp, who gave him a gift he didn't really know what to make of yet felt compelled to keep. But other than that, there isn't really anyone who's come close; and everyone who approaches him with friendliness ends up having ulterior motives. 

And then comes Tod Clifton. Immediately, the reader can tell the narrator feels something differently about him, because we get a... strangely lengthy and... specific description of his physical presence. The narrator, in a sort of instinctual response, feels his position being threatened by Clifton, a reaction that quickly dissipates when he sees how invested in the cause Clifton is. Although it's never explicitly said, the narrator seems to have an actual connection with Clifton, something that he has yet to get from others. This position is only solidified by the subsequent fight scene and confrontation: even when Ras the Exhorter starts agitating the both of them with his harsh words about the Brotherhood, there is no immediate rift between the two, no verbal quarrels.

And then he disappears. And the reader sees the narrator show genuine concern in the scenario, immediately forgetting his own personal ~woman~ problems and even slightly cursing himself for not keeping a closer eye on Clifton. And when the narrator does see him again, peddling a racist caricature doll, he seems genuinely distraught: "'Not you...' I began. But his eyes looked past me deliberately unseeing. I was paralyzed, looking at him, knowing I wasn't dreaming..." (432). While one could chalk this up to the narrator being shocked by the casual racism again, I think it goes deeper: yes, he's shocked by the Sambo doll, but he's more shocked by the fact that it was Clifton, a man who he clearly respects and trusts, someone he thought was better than where he ended up. And Clifton himself seems to be disappointed by the narrator's appearance as well: note the term "deliberately unseeing", worded in a way that almost makes it sound like Clifton feels humiliated being seen by the narrator (again, someone who he respects) in this position. The whole incident makes the narrator feel very shaken up, as he starts questioning how this could have happened to someone with so much to gain (unfortunately, it also makes him hold on even tighter to his faith of the Brotherhood, for fear of being lost).

And then he gets shot. And again, even though the narrator has seen plenty of horrors in his life, Clifton bleeding out on the sidewalk is something that hits him extremely hard, harder than if it was somebody else. He tries to go and help him, even calling Clifton "a friend" when the cop tells him to leave.

It's interesting: directly following Clifton's unfair demise, the narrator has one of the largest contemplative moments in the book. He continues wondering just why Clifton chose to fall to the level he did, and why he felt the need to die for such a useless cause. The entire scene with him watching the dancing Sambo doll, trying to find the meaning in the madness, is, in my opinion, one of the most somber yet saddening scenes in the book. For the first time, the narrator breaks down to his most human: he cries for Clifton, crying from the injustice, the ability of "them" to "use a paper doll, first to destroy his integrity and then as an excuse for killing him." (448)  

Clifton's death was a turning point both for the narrator's point of view and for the book itself, as the narrator, for the first time since joining the Brotherhood, takes matters into his own hands to organize the funeral and do justice to his fallen friend. He falls into a sort of work-focused depression, forgetting to eat and sleep, focusing completely on his independent duty to honor Tod. And during the eulogy, the narrator has a perfect opportunity to push his agenda, and if it was anyone else he would. But he can't. He just can't bring himself to taint the procession with the Brotherhood. Instead, he goes in frantic, angry circles, hammering in the pathetic injustice in Clifton's death. The narrator is moved not to preach the ideologies he's been taught by the cult that took him in, but to tell the truth about the system as a whole: 

His name was Clifton, and they shot him down. He was shot by a cop who was all too ready to kill a black man, and the police force needed only to spout their same tripe to sweep it under the rug. Clifton will be remembered not by who he was but how he died, and even if you cry, even if you scream in anger and curse the gods, eventually you will go home, and you will forget.