My favorite "crazy theory" is that the Paleocene–Eocene Thermal Maximum (PETM) was caused by a previous industrial civilization that, like us, found a bunch of easy to access hydrocarbons, naively dug them up and reached the same climate change problem that we did, ultimately wiping them out.
Of course there is 0 evidence for this at all, but it was also more than 50 million years ago. If you look into it basically nothing about an advanced industrial civilization would likely survive to make it into the geological record for us to observe. The only reason to even entertain this hypothesis is that the PETM also experience a very rapid increase in atmospheric CO2 and we aren't entirely sure why.
Unfortunately this means that there's probably not much chance for a rich field of xenoarchaeology to exist since it's not even possible to do this on our own planet.
What is an interesting thought experiment is: Suppose we realized we as a civilization were doomed and wanted to sent a message to future industrial civilization on Earth warning them about being too aggressive with hydrocarbon usage. To my knowledge there is no known method to ensure a message could be sent that far in the future, but it's fun to try to think of ways we could send a message to a future, essentially, alien civilization here on Earth.