No, they do not need to send anything if they do not elect COBRA. Once their election rights expire, they are no longer eligible to elect COBRA.

The individual has 60 days to elect COBRA coverage.; The 60 day period begins on a) the date the individual would lose coverage as a result of the qualifying event, or ...

Yes, each qualified beneficiary has the right to an "independent election" of COBRA. For additional information, see page 5183, Question 6 of the 1999 Final COBRA regulations.

If the individual has not returned the election form within the election time frame, they are no longer eligible for COBRA coverage. If they have not already been terminated from coverage, ...