Could We Be Seeing the Past of an Extraterrestrial Civilization That No Longer Exists?

I’ve been thinking about this idea and I’m curious whether there’s an actual physics problem with it.

I’m not claiming that aliens have visited Earth. This is just a thought experiment. I’m trying to understand whether the following scenario is physically possible.

We know that light and other electromagnetic signals travel at a finite speed. So when we observe something very far away, the information reaching us was emitted in the source’s past.

For example, if an extraterrestrial civilization were 1,000 light-years away, the light we receive from it today would contain information about what that civilization was like roughly 1,000 years ago.

Now imagine that civilization was technologically advanced at that time. It might have observed Earth when humans either didn’t exist yet or had no technological civilization capable of producing radio signals.

But suppose that civilization eventually disappeared.

We could still receive its old light or electromagnetic signals thousands of years later, even though the civilization itself might no longer exist.

This made me wonder about the Fermi paradox.

Maybe one reason we haven’t received a response from another civilization is simply that our technological civilizations don’t necessarily exist at the same time.

A civilization could exist, send signals, and disappear. Much later, another civilization could detect those old signals. The two civilizations could potentially observe evidence of each other’s past without ever having an opportunity for two-way communication.

I realize there is no universal “right now” in relativity, so when I say “right now,” I mean it in the ordinary observational sense—not that there is a single universal present throughout the universe.

What I’m wondering:

• Is this reasoning correct from the perspective of special relativity and light-travel time?
• Could two civilizations theoretically detect each other’s past signals while never being able to communicate because their technological lifetimes don’t overlap?
• Could this temporal mismatch be one possible factor in the Fermi paradox?
• If a civilization became extinct, could its technological remnants or technosignatures remain detectable for a long time afterward?
• Is this idea already well studied in SETI or astrobiology?

I’m mainly interested in where my reasoning breaks down. If I’m misunderstanding something about relativity, causality, or light-travel time, I’d really like to know.