IPA: //ʌnˈsaʊndli//
KK: /ʌnˈsaʊndli/
In a way that is not based on good reasoning or is not reliable.
The decision was made unsoundly, leading to many problems later on.
Unsoundly → It is formed from "un-" (meaning not) and "sound" (from Old English "sund", meaning healthy or safe) and "-ly" (meaning in a manner of). The word "unsoundly" means in a manner that is not healthy or safe.
Think of 'not' ('un-') being combined with 'healthy' ('sound') to remember that 'unsoundly' means acting in a way that is not safe or healthy.