I was fighting several monsters at a time, two goblins and two rats if I remember right. I was killed by one of the goblins, but the game hanged when showing the "...killing you!" message. The death popup never came up. I had to close JADE using the Task Manager. Might be something like the second gobling wanting to attack me after I died, but that's just a guess.
I just reproduced this, but my PC was only directly engaged with a single monster (five-headed hydra). There was another hydra and a ruffian waiting to fight me behind the first hydra, but I wasn't adjacent to them when I was killed.
Same as Laukku's report; no pop-up came up when I received the "...killing you!" message, and the game wouldn't respond to any commands.
I also had to kill the window via task manager (I'm running JADE 0.1.2 on Windows XP)
There was a problem when monsters without any professions killed you. They thus had a total profession level of 0 (multi-classing already is in the game even if it's not yet available for the PC) which lead to a problem with calculating the level advancement.
Fixed for JADE 0.1.3. Please send your real name to creator(at)ancientdomainsofmystery.com for it to be included in the credits.