Now if your average alien society lasts for a long time — say more than 100,000 years — then its signals can cover the entire galaxy while the aliens are still with us. If this is a typical situation — if Klingon cultures have staying power — there could be many transmissions wafting over the Earth from societies that are still extant.
On the other hand, if the lights go out for most societies relatively quickly, then most signals reaching Earth now or in the immediate future are likely to be from aliens who are dead. If most civilizations transmit for 10,000 years (we earthlings have been transmitting for roughly a century), then 99 percent of all the signals washing over our planet are from expired, or at least silent, societies.
So yes, a SETI detection might come from a fossilized culture. But it’s fair to ask, “So what?” Would we care that the aliens are gone? Obviously, back-and-forth conversations would be out of the question. But conversations would be tedious anyway if the aliens are as much as 100 light-years distant.
And besides, I read Julius Caesar in high school Latin class, and it was interesting even though the “message” was 2,000 years old and the Roman Empire was dead. If we were to receive a message from aliens, the big news wouldn’t hinge on whether we were able to converse with them. It would be simply that someone else was out there.
Any message we receive would come from a society whose technology was far beyond our own. After all, they were able to transmit an intelligible signal powerful enough to reach across the cosmos. And so I believe that whether or not they were still around, what they had to say would be enormously interesting — and possibly useful in ensuring our own long-term survival.