1. Continuation of the status quo. The DPRK stays a basket case and continues lashing out locally but nothing major happens.
2. Hot war breaks out (precipitated by the DPRK or the South or the US), the North loses fairly quickly, there are catastrophic civilian casualties in the South and the North and perhaps elsewhere (e.g. the North launches a nuke or chemical weapons or what-have-you against Japan or the US, just 'cause it can), American military losses are comparatively minor in comparison to everything else. Ultimately, the industrial base and economy of the Korean peninsula is in shambles and is all the worse for having to deal with bringing the North into the 20th (let alone 21st) century, despite lots of foreign aid it's still a shitty situation for a lot of people for a long, long time.
3. The DPRK regime falls from within relatively peacefully. The North and South reunite and a crap-ton of effort and struggle is necessary to bring the North out of the dark ages. It's a crappy situation except for the Northerners who had been abused and/or starving, but it's still a hell of a lot better than option 2.
4. China forces the DPRK regime to step down through some means and takes over control of North Korea (either via direct annexation or through proxy control). Hostilities in the region diminish greatly and conditions improve for the North Koreans. It's a crappy situation but still better than option 1 or 2.
There are lots of other things that could happen, of course, but I think these options take up the bulk of the probability space.