This is one of those national rules subject to interpretation by each section. This is from the Norcal captains' handbook, and seems reasonable to me:
(bold emphasis is mine)
1. It rains but no match has started:
The away team arrives, captains exchange line-ups, everyone is warming up, no one has started, it rains. When the match is rescheduled, the teams can use totally new line-ups. Any defaulted individual match disappears.
2. It rains after any individual match has started:
The away team arrives, captains exchange line-ups, two individual matches start, it rains. (Remember, if even one ball has been put in play (not warm-up) in your team match, the match has officially started.) When the match is rescheduled, the players who started in those two individual matches return and start exactly where they left off. For the remaining match or matches that did not start, the captains may use different players. Any defaulted individual match stands as a default.