My fantasy species has the ability to swallow small to medium appendages whole. They're known for biting off and swallowing hands and feet. A snake like jaw could work but how would it still maintain a somewhat human-like face?
Oh, I think we can get 'er done.
Your critters look ... basically humanlike, but they all seem to have big jowls and double or triple chins. No biggie, right? Well, when it becomes time to swallow a large body part, they throw their heads back, and jowls/underchin area balloons out (think when a humpback whale takes a gulp of krill) to make room.
To address @l-dutch concerns, these guys will have a cartilaginous sternum instead of bone, so they can expand there as well.
Now what I'd be worried about is that the big eaters of the animal kingdom tend to get sleepy after gulping down massive body parts. It'd be awkward to have afternoon meetings at work. Though it could be worse...
"Hey, haven't seen you for awhile. How was your date with Mindy?"
"Well, she took the waiter's arm off at the shoulder, swallowed it whole, then passed out into the mashed potatoes. She's been asleep for the past three weeks."
"So what you're trying to say is that you didn't get to second base?"
"Yeah, pretty much."
Apart from dislocating the jaw, the main problem is that we humans have a 90 degree turn when going from the mouth cavity to the esophagus. Sword eaters solve the issue by looking upwards, but I am not sure that would be doable with a dislocated jaw.
Another problem when swallowing a whole body part is going to happen once it has to pass through the rib cage.
The present structure of the human rib cage is closed, meaning it cannot expand that much. So the esophagus is limited in the size of objects it can carry.
These humanoids would have evolved to eat large amounts of food when it comes, (ie. food is abundant, but only at certain times, or in other words, feast or famine).
In both anime and cartoons, there seems to be a tendency to give people big heads. This would be pretty much perfect for our purposes, along with the following modifications:
A gape, AKA a serpentine arrangement of skull bones, ligaments, and muscles.
More cartilaginous structure (jaws, collarbone, sternum, ribcage, and so on) to allow consumption of huge amounts of food.
Expansive stomach and esophagus (like a gulper eel), along with strategic
Why a big head? Because big heads means bigger jawbones, which means larger gape. Granted, it won't be a huge difference, but every little bit helps.
This arrangement will allow your humanoids to swallow not only part of an arm, but an entire person. I can see it now:
Mindy: Hey, Yancy's coming over here, and she looks upset. Did you say something to her?
You: No, I can't imagine what I could have said to upset her....
Yancy stops in front of Mindy. Mindy steps toward her, about to ask her a question, and then Yancy's mouth suddenly distends horribly, clamping down over Mindy's upper body (head, chest, shoulders) and her arms grab and lift Mindy as she swallows. In mere seconds, Mindy has been swallowed whole.
Congratulations, you happened to get yourself claimed (albeit unknowingly) by the one girl who A) was a yandere just waiting to happen and B) just happened to be part of the Hominem Edacem Sapiens subspecies. What happens next is up to you, but if I were you, I'd exchange small talk until she drops her suspicions (of you planning to leave the country), then leave, change your name, and leave the country.