By any measure, Arsenio Hall was a Hollywood success: He had starred in popular films, packed houses as a stand-up comic and hosted a hit late-night television show bearing his name.

Donald J. Trump saw it differently by the mid-2000s. In his eyes, Mr. Hall was nothing.

“Dead as a doornail,” was his assessment of Mr. Hall in a previously unreleased interview from two years ago. “Dead as dog meat.”

Why such a harsh judgment? Because in Mr. Trump’s eyes, Mr. Hall had suffered the most grievous form of public humiliation: His celebrity had waned. His star had dimmed.