An expression used to strongly deny that something should or could happen; used prenominally to modify a noun (that ... should not / cannot possibly ...).
彼は嘘をつくはずのない人物だ。
He is a person who could never lie.
こんな簡単な問題を間違えるはずのない学生が間違えた。
A student who shouldn't have made such a simple mistake made one.
その証拠は偽造されているはずのない資料だったが、調査の結果、改ざんが見つかった。
The evidence was supposed to be material that could not have been forged, but investigation found alterations.