Elsie. After winning the leftover challenge, she got the cold shoulder from the other competitors (Jessica, Ralph and Michael) and couldn't get their help. Even after a motivational pep talk from Ramsay, she floundered badly. When it came to elimination, she and Jessica were up for grabs and Ramsay, having observed the cold shoulder that Elsie was given, asked whether or not she got support... and she said that she did.
Season 2
Virginia. She was despised/alienated by Keith and Heather for allegedly receiving favoritism from Ramsay, even though, regardless of whether this true, it wasn't her fault at all, and she had never been anything but nice to the other contestants. She was also sabotaged by Sara, and had to deal with her team demanding bribes in order for them to work for her in the finale and the survivor's guilt she had over constantly dodging the bullet and wondering if she did deserve to be there.
Larry, mostly for being the first ever contestant to be medically evacuated, but he was also The Chew Toy and didn't get treated particularly well during his short stay on the show.
Julia. While she became very popular in the fans' eyes later, the first episode made you feel like any other new kid at school being left out due to her background as a Waffle House chef. Tiffany struggled with the quail eggs and Julia wanted to help, and she knew that the Red Team had problems with communication but no one came to Julia's aid. In the confession, she's tearing up and when Ramsay asks what's wrong, she cries "I just want to cook!" Poor girl.
Season 4
Christina for being targeted by the red team for purely personal reasons, claiming that they found her condescending. The real kicker is that earlier, Corey, and later, Jen, were both much more condescending than Christina could ever hope to be.
Season 5
After a bad dinner service J barely escapes being eliminated, and after that, he is shown looking at pictures of his family and explains via Confession Cam that he was on the show for his wife and son (who had been diagnosed with autism), and ends up in tears. At that moment, it's hard not to feel bad for him.
Season 7
Salvatore was tasked with taking orders from the diners. His orders came in written incomprehensibly. Ramsay screamed at him, "Didn't you go to school?!" and Salvatore replied, "No, Chef." He explained after he arrived in America, he worked to help his family and never went to school. Ramsay was so stunned he stopped scolding him and told him to "Just take your time."
Holli counts despite being the winner, considering the fact that she never actually got the job at the Savoy Grill, despite winning the competition. Apparently, a law in the United Kingdom forbids the employment of foreign applicants as a prize from winning a competition, which was most likely a mistake on the producers' half for not taking the time to look into it (it was a new law that had gone into effect while Season 7 was being filmed). Nevertheless, it's hard not to feel bad for the winner of the entire show not even getting the prize they were promised from the start of the season, especially when you read this article in which Holli expresses disappointment about not being able to move to London and start a new life.
Siobhan due to her having a Dark and Troubled Past of growing up in a broken home and later ending up homeless after leaving the show.
Season 10
Barbie is this in the eyes of some fans, and only two episodes in, no less. At least one third of the red team (ESPECIALLY Tiffany) absolutely explodes anytime she does something. Barbie is not the best chef by any means, but her mistakes aren't any worse than the rest of the red team's mistakes.
Roshni. Getting stranded on a zip line while her teammates thought it was hilarious (though they did help her down), being put up for elimination even though she didn't deserve it... and finally being eliminated in the eighth episode when it came down to her and Patrick, many felt that he should've been eliminated instead, considering how poor his leadership skills were. At least she held better success in Chopped.
Season 11
Jon. Pretty much any clip from Season 11 will have people in the comments expressing Sympathy for Jon. The reason? Jon is a pretty competent and talented cook who had the misfortune to be paired with what is near-universally agreed to be the worst Blue Team in the entire history of the show. Many felt as though he didn't deserve to be kicked out in the Final 3, and that he should have won the season, or at least made it to the final episode.
Mary got this too. Sure she got second place for the whole season but it was mostly due to Dan that she lost. The kicker? He apologizes for being a jerkass and promises to make it up - which he should've done earlier at the service!
Season 12
Rochelle, especially after episode 11. During punishment, she confesses that she wants to start a family and her team ostracizes her a bit because they feel like she's not really giving it her all and isn't serious about the competition. Then she's the deciding vote between two people in the Blue Team (having transferred there) and then has a minor meltdown prior to the "create a menu" dinner service and having Richard and Gabriel wanting to kick her out due to that meltdown. The road for her is gonna be tough. What doesn't help was that she was eliminated in "Four Chefs Compete" and she won't be able to keep her jacket (Melanie would instead). Damn it.
In a sort of Pet the Dog moment, Jason considered voting against her, but decided not to, saying she was too much of a badass that night.
Scott didn't have a much easier road. He was constantly nominated when he didn't deserve it - like Joy nominating him simply because she didn't want to nominate her friend Kashia (even though Kashia deserved to be gone far earlier than she was), and Anton always blamed him for Anton's own mistakes. Joy's treatment of Scott was especially grating because Scott was only ever nice to her (even consoling her during her Heroic BSoD).
Season 13
Sterling is seen as this, due to neither team taking him seriously and always doubting his skills despite the fact that, goofy tendencies aside, he has proven himself in the kitchen time and again.
Season 14
Michelle can't seem to open her mouth without getting condescended to by her teammates, despite being a fairly competent chef.
Season 15
Manda. She's a young mother who's clearly been through a lot (she used to work as a stripper to pay her bills), clearly misses her children (she's almost in tears the last few times she mentions them), and has next to no self-confidence, yet never gives up or loses her upbeat attitude. It reaches its peak when she injures her back during a punishment and gets No Sympathy from her team during service, who berate her for being too slow while also making her do most of the work despite all of the pain she’s in, until Chef Ramsay calls them out for not helping her while she’s struggling. She isn't the best chef, but she doesn't deserve the way Frank treats her like shit or how Dannie talks down to her.
Season 16
Aaron. Despite being acknowledged by Ramsay himself as a competent cook, he received very little respect from his teammates due to his inexperience and young age, along with being too quiet and uncommunicative in the kitchen. Of his three nominations, only one was a result of mistakes in actually serving food, and in the third that resulted his elimination, he had a perfect service. He's essentially a male version of Season 14's Michelle (points for both being 22 while competing) that happened to be a bit quieter and less assertive. Unfortunately, that difference contributed to his much earlier elimination.
Season 17 (All Stars)
Arguably Josh. While he was probably the weakest chef in the entire competition, the fact that the red team (most likely) didn’t even give him a chance to shine with them demonstrated his loneliness. As he put it, “There’s no green team to go to so I just feel like I’m alone.” Makes his elimination during service a lot more upsetting.
Season 18 (Rookies Vs. Veterans)
Chris revealed in the second episode that he had an accident which damaged 90% of his face a few months before the competition and has since been suffering from memory loss. After a few services, his confidence dropped dramatically and his anxiety came creeping back, and despite cooking the best dish of the challenge and the red team trying their damnedest to get him to bounce back, he made the decision to leave in Episode 6.
Season 19 (Las Vegas)
Nikki. She was nominated during the menu challenge for failing to clean her shrimp properly, then broke down crying during service after her lobster was sent back for being undercooked, only being saved by the gross incompetence of Kenneth and Eliott. This turns her into an easy target for having the least experience of anyone on the red team. To her credit, Nikki improves dramatically to the extent that Ramsay pulls her into the pantry to personally offer praise. When Nikki is finally eliminated, Ramsay offers her the opportunity to stage at any of his restaurants in the world with all expenses covered.
Season 21 (Battle of the Ages)
Tara. This woman had it rough when the format was switched back to the Battle of the Sexes in Episode 3. Not only did she see Nicole and Mindy get eliminated early on, but she was stuck on a team that had a very low opinion of the 40-Somethings and were gunning to send her home. Not only that, but she felt betrayed when Alex used his Punishment Pass on her to take her spot on an reward (though to be fair, Alex did not do it out of spite but more out of a misjudgement).
in which Holli expresses disappointment about not being able to move to London and start a new life.