In the latter situation, the script supervisor is expected to record in their notes that a pick-up shot was called for (so the film editor can understand and correctly edit the resulting footage) and also help prompt or "cue" the relevant actor by reading the last line before that actor's line.
It is increasingly common for a director to not immediately call "cut" after a blooper, but instead leave the camera rolling and call for a pick-up, which makes pick-up shots an exception to the normal rule that a script supervisor does not cue actors while the camera is rolling.
[1] Pick-up shots and re-shoots can also occur after principal photography is complete—after continuity, logic, or quality issues are identified during the film editing process.
In other words, they can occur months after the sets have been struck, the costumes and props have been stored, and all the cast and most of the crew have moved on to other projects.
[2] In deciding whether to proceed, the director and producer must carefully balance the substantial expense of reuniting key cast and crew members on set against whether pick-ups or re-shoots are absolutely necessary to fix plot holes (or worse) in the final cut.