Overthrow Clarification

[BillM.]

ASA Rule 8-5-G:
“When the ball is live and becomes overthrown or is blocked:
EFFECT: All runners shall be awarded two bases. The award shall be governed by the position of the runners when the ball left the fielder’s hand. Runners must return to touch a base missed or a base left too soon. When two runners are between the same two bases, the award is based off the position of the lead runner. Once a base runner advances to the next awarded base, the runner may no longer return to touch any based missed or any base left too soon.
Exception: When a fielder loses possession of the ball and the ball leaves live ball territory:
EFFECT: Each runner is awarded one base from the base last touched at the time the ball entered the dead ball area or became blocked. “

Can you fine folks clarify the underlined exception for me, including an example?

The way I am reading this is that if a fielder has possession of the ball, but then drops it, and it rolls into dead ball territory, the base award will be 1 base from the moment it rolls into dead ball territory. In my limited experience (3 years) I haven't seen that happen, so I am just trying to prepare myself for our season starting in a few weeks.