Directors of long running shows and their involvement with replacements, etc. and the show long term?

Shoshana Bean was on Jesse Tyler Ferguson’s podcast “Dinner’s On Me” recently. They talked about her replacing Idina in “Wicked” and how she was a standby before being a replacement. She took over and was multiple months into the role when Joe Mantello came to check in and was surprised that it would be that long before he came to work with the replacement. I know that there’s a team under a director to keep working with the cast and replacements but how much does Joe Mantello (Wicked), Rachel Chavkin (Hadestown), Walter Bobbie (Chicago), Julie Taymor (Lion King), Sam Pinkleton (Oh, Mary), Casey Nicholaw (Book of Mormon), Moulin Rouge! (Alex Timbers), Christopher Wheeldon (MJ), & Juliet (Luke Sheppard), Danya Taynor (The Outsiders), Thomas Kail (Hamilton), etc. remain involved in their shows? Also because they get paid for their direction in perpetuity, yes?