I think this MOD may work for what you want. While it doesn't let them log in without a ticket number, it will return them a list of their tickets to their email. You can always change the verbiage so that you aren't making your customers feel like they have done something wrong by "forgetting" their ticket numbers.
http://osticket.com/forums/showthread.php?t=2729&highlight=forgot+ticket+number(http://osticket.com/forums/showthread.php?t=2729&highlight=forgot+ticket+number)