For an example of when a dam is teetering upon catastrophic failure, with operators stuck between a rock and a hard place, see the 2017 Oroville Dam crisis: en.wikipedia.org/wiki/Oroville_Dam_crisis

This was covered in a Plainly Difficult video on YouTube, as well as other channels like Practical Engineering (also on YT).

Essentially, in that situation, the operators were discharging water until they found the main spillway was becoming damaged (uncovering shoddy work from decades ago). But the amount of rain meant that using the never-tested emergency spillway might actually damage the dam foundations. So in the end, they had no choice but to use the main spillway, as the less worse of two awful choices.

Known only after the fact, 2017 was a particularly wet year in California, coming after years of drought conditions. So holding onto water within the reservoir wasn’t imprudent. But a flaw in the main spillway, and lack of testing of the backup, made a bad situation worse.