An offence during the dead-ball interval is a separate event
Law 8 states that an offence while the ball is not in play does not change how play is restarted. A player can receive a card during the interval while the originally awarded throw or free kick remains the restart.
Imagine Team A already has a free kick. While the ball remains stationary, a Team B player protests and is cautioned. Team A then takes the same free kick from the same location. There is no missing second foul restart to reconstruct.
Keep two columns in the incident record
One column records why play stopped and where it will restart. The other records misconduct while it is stopped. A card graphic usually belongs to the second column in this example; it does not automatically overwrite the first.
Timing matters. A superficially similar action after the ball returns to play can raise another restart question. Watch whether the ball had actually been put back into play before describing the conduct. The original example explains the dead-ball interval and does not suggest that all later actions share an identical sanction. It shows how the same restart can survive an additional disciplinary event.
Questions answered
Does a dead-ball caution automatically create a new free kick?
No.
What timing detail should the replay preserve?
Whether play had restarted before the later conduct.
Sources & further reading
Official references for the subjects discussed. Service terms and device software can change.