To summarize and add to the good and accepted answer. Abandoned buildings can possibly be brought back to life, but it takes a long time. Especially, comparing to how fast they can be abandoned if necessary conditions are not met. They can be brought back from any condition (from simply vacant to damaged by fire), and, possibly, it takes different amount of time given the same demand (or higher threshold of demand) to get repopulated.
Aside from negative implications of leaving abandoned buildings standing, as outlined in another answer, it is possible for them to fall into such state of disrepair that they completely collapse (it takes a long time as well), turning into pile of rubble further driving the land values down, and contaminating the environment. There could be additional icons associated with such ruins (for instance, indication of toxicity), and they should be promptly removed.
Abandoned buildings and ruins can be easily identified in multiple views, but most convenient way to do so is by using the “Bulldoze” tool. The amounts of such buildings would be displayed in the bottom right corner. And they can be seen on the map as a bulldozer for ruins (left side of the image below), or a boarded-up house for abandoned buildings (right side).