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.