From Ryan: If I fall during delivery, can I hold on to the stone and re-try?
A: If the delivered stone has not yet touched the tee line closest to you, then yes, you can hold onto the rock and start over without penalty.
Rule R5 f:
“A stone is in play when it reaches the tee line at the delivering end. A stone that has not reached the tee line at the delivering end may be returned to the hack and redelivered.”
So let any newbs playing know that if they slip out of the hack, they can hold onto the rock and throw it again if it hadn’t touched the tee-line. And if the other team tells you that is not the rule, then just cite R5 f from Curling Federation Rulebook.
Source: http://www.curldc.org/about/WCF.Rules.June2010.pdf