Definitions of unsound:

• adjective:   not sound financially

  Example: "Unsound banking practices"

• adjective:   not in good condition; damaged or decayed

  Example: "An unsound foundation"

• adjective:   of e.g. advice
• adjective:   suffering from severe mental illness

  Example: "Of unsound mind"

• adjective:   containing or based on a fallacy

  Example: "An unsound argument"

• adjective:   physically unsound or diseased

  Example: "An unsound limb"

• adjective:   in deplorable condition