Usage patterns
〈事〉が不安定になるfor something (a situation, economy, etc.) to become unstable
Recently, the economy has become unstable.
不安定な〈事〉an unstable situation, condition, or state of affairs
Unstable weather has been continuing.
〈人〉は精神的に不安定だsomeone is emotionally/mentally unstable
He has been emotionally unstable lately.
〈物〉が不安定に揺れるfor a physical object to sway or wobble precariously
That chair has short legs and wobbles precariously.