This might be the rule you are looking for:
108c. Missed Frames
A player who starts a game and then misses frames due to an emergency may return to bowl before
completion of the same game and make up the frames missed, unless the league rules:
1. Require a player to enter the game at the frame being bowled by the team.
2. Do not allow a player to return to bowl.
Rule 108a must be applied for missed frames that are not made up in the same game.
This is how I would apply the rule:
A member can leave a game due to emergency and return. If the bowler returns before the end of the game, they may make-up the missed frames. If the bowler is not available till the start of the next game, then rule 108a. applies for the end of the previous game.
108a. With Cause
When a player is unable to complete a game because of disability, injury or emergency, and another
eligible player is not available, the team shall count the actual score for the frames bowled plus onetenth
of the league’s absentee score for each frame missed. (See Rule 118a for average information.)
NOTE: For computing score: Take actual score for frames bowled; for a strike or spare in last frame
bowled credit 10 pins. Add 1/10 of league’s absentee score for each of the remaining frames.
For example, if absentee score is bowler’s average less 10: Absentee score, 145; 1/10 of 145 =
14.5 x 3 frames = 43.5. Drop fraction and add 43 to actual score for 7 frames bowled. The
fraction is dropped after the total amount is figured, and not from each frame.
As with many rules, there is some level of interpretation.
