If Throne Room or Procession was played on a Hireling and the Hireling leaves play, does the modifier stay in play?

Question

Accepted Answer

Yes. The Throne Room or Procession stays in play, and if the Hireling leaves play the every-turn effect still happens. Whatever later removes the modifier does not stop the Hireling's every-turn effect.

Dominion: Intrigue

If Throne Room or Procession was played on a Hireling and the Hireling leaves play, does the modifier stay in play?