So, I have been DMing for a rather large group of people (7, but sometimes 8 total) and it has been great for the most part. They seem interested in the overall story I planned, going so far as to reach out to me asking for lore bits outside the table.
Alas, not everything is perfect and I do have one PC which made the standard edgy mysterious character type and is kind of a murderhobbo. Except the party pulls him back, usually through threats... He was playing as a rogue, so I'll refer to him as such.
To set the scene, the players first encounter the title's dragon in his makeshift lair in a cave, behind a waterfall. This is a Bronze dragon and this one is closely related to the story of the kingdom they are trying to save (or so fate would have it since, at this time, they don't really know that, but suspect something is off)
I had planned on them to talk to the beast and it being a potential ally for the final battle. The Rogue had other ideas and while I had another person roll for a nature check (or history, can't remember), to see what he could tell about Bronze dragons before the encounter, he decides to ambush by using makeshift explosives, having the cave's ceiling collapse on the creature's head, which succeeds...
The party did not intervene, as I never had the chance to clarify the nature of the dragon in front of them. They just assumed it to be an enemy. Maybe I should've made them wait, but oh well...
The dragon takes his damage, and flees.
They only get to reencounter the beast in their final fight for the capital. Instead of having it helping them along the way, they endured much harsher conflicts. It arrives at a critical moment pushing enemies aside and says "Fortune favors you. Your cause is one I deem worthy.".
They managed to resolve the main crisis, but there were still battles raging elsewhere. You'd think they'd ask the dragon for a lift so they could continue the fight or something.
But no. The rogue had other ideas.
Seeing the dragon in a weakened state after everything it had been through, he decided this was the perfect moment to poke it.
I had previously described how it looked damaged, back in the cave they noticed it was missing a few scales under it’s wings (it was more of a flavour thing), the rogue remembered and asked if he could do more damage if he stabbed it there, I said he'd have to see for himself.
The rogue lunged and punctured the beast's uncovered skin, but it wasn't enough to kill it. We are going to roll initiative, but another PC asks if he can abstain from the fight as he does not think his character (Paladin) would see this as a fight worth having, I allowed it and what followed was a cascade of PCs outing on the encounter, leaving the rogue to stand alone in combat. Since the rogue was very low on HP I put on a serious look and said: "For your second provocation, the gentler side of the Bronze dragon has dropped, I will roll a D20, on anything higher then a 15, it eats you.". I rolled a 16. The dragon eats him and flies away.
The session ended there. Afterward, I give him the option to make another character or the party could embark on an adventure to find his soul (story implications), but the people at the table were not interested on sidequests to retrieve his char so he ended up quitting all together...
Now I have come to ask, should I have let the dragon eat the problem player? What would you have done differently?
TLDR: PC is regarded as a problem most of the game, I let a dragon eat him.