Such situations are monitored by setting up laser rangefinders around the site, and measuring the distance and angle to key points high up on the structure. If these points hold position over time, even with aftershocks, engineers may decide the building has worked itself into a temporarily stable position. It's analogous to the angle of repose that a pile of gravel assumes when emptied out the back of a dump truck.
Gravel finds its resting angle in seconds, but settlement is slower in complex structures, particularly when (as in the World Trade Center) a fire is progressively weakening the frame. When researching the WTC collapse for the special edition of Inviting Disaster, I was struck by comments from witnesses about sounds they heard in the South Tower. This snip from my book:
"It's a peculiar fact that buildings that are about to collapse often give audible warnings of distress minutes or hours beforehand, as gravity loads shift away from failing columns and girders. Some people in the stairwells in the South Tower heard these spooky noises of impending failure. One man compared it to the crackling sound a handful of uncooked spaghetti makes when snapped during preparation of dinner."Meanwhile, demolition companies have offered suggestions on what to do with the Grand Chancellor, if authorities decide to bring it down. This one suggested a large crane to drop a headache ball on the structure. We can expect many novel ideas if the situation goes on.
Conventional demolition of skyscrapers, not likely in this case, relies on crews who take it down one floor at a time, or on experts to place explosive charges among the supports. A vital tool for such work is the linear shaped charge - see my post on that.