Amazingly, for someone so eager to give a lesson in linguistics, you managed to ignore literal definitions of the words in question and entirely skip relevant information in my (quite short) reply.
Both are widely used in that context. Language is like that.
Further, the textbook definition of Stability-
the quality, state, or degree of being stable: such as
a: the strength to stand or endure : firmness
b: the property of a body that causes it when disturbed from a condition of equilibrium or steady motion to develop forces or moments that restore the original condition
c: resistance to chemical change or to physical disintegration
Pay particular attention to "b".
The state of my system is "running". Something changes. If the system doesn't continue to be state "running", the system is unstable BY TEXTBOOK DEFINITION.