It always emboldens the mob. They aren't after an apology, they're pursuing harm against the target and typically won't stop until they get it - unless you can

It always emboldens the mob. They aren't after an apology, they're pursuing harm against the target and typically won't stop until they get it - unless you can show strength to the bully behavior and can stand-off against them (which not everyone can do). If you can, they'll give up and pursue another easier target. The mobs have weaponized job firings, which puts most people in a position of immediate weakness where they're afraid to stand their ground.