LORELAI: My heel just broke off. Damn, these are brand new shoes, too.
RORY: They were made in 1943.
In the final hour of the marathon, the heel breaks off one of Lorelai’s vintage shoes. The rules of the contest didn’t require participants to wear shoes, and as they have less than an hour to go, Lorelai and Rory could have kicked their shoes off and finished the marathon in bare feet.
Instead Lorelai uses her yellow emergency card, which allows her a ten minute break to get her shoe repaired. During this time, her partner must stay on the floor and keep moving. However, Rory has been dancing for twenty-three hours, and is far too exhausted to stand upright and keep moving on her own.
Lorelai gets Dean to hold onto Rory and keep her moving until Lorelai returns. We know that Dean doesn’t care for dancing, but this is the third time in three seasons he dances with Rory – the other two times were at her school dance, and for her debutante ball (including the dance practice before the ball). There isn’t much involved this time, all he has to do is keep her upright, and he soon says he’s quite enjoying the experience.
When Taylor announced the rules, he never said it was possible to get someone else to dance with your partner during their break if they were physically incapable of standing without assistance. However, he never says it is actually forbidden, either. As usual, Lorelai is very ready to exploit a loophole in the rules if it is to her advantage. (And Kirk has been shown to be playing dirty as it is).