I was recently on a flight - the aircraft was a 737-800 - where I had a good view of the front of the left engine. The situation in the title did not occur, but it seemed awfully close.
After pushback, while the plane was waiting to start taxiing under its own power, I looked at the tiny waterspouts sporadically forming in front of the engine (it'd been raining all morning). And then I noticed a piece of caulk (or tar or whatever it is) was being lifted from between two concrete slabs of pavement.
The strip of caulk looked like it might have been 30cm long and 2cm in "diameter" (it had a more rectangular cross-section, but you get the idea). It was still attached at one end, but it was directly in front of the engine, and its free end was being "tugged" up toward the intake in fits and starts, sometimes standing straight up.
Thankfully, it never went further than that. I considered alerting the cabin crew, but everyone was already buckled in, and I really didn't want to cry wolf on a airplane (so to speak). Still, I was very much considering it just as the plane started moving without any further drama.
As soon as we were in the air, I discreetly told a flight attendant, and she told the pilots. She came back a little later asking for a few specifics, so I imagine the pilots were radioing the airport we'd just left.
And I got a free cup of coffee (yay...)
My question is: What might have happened if that piece of debris had come loose and been ingested by the engine?
I wouldn't expect it to be catastrophic or anything (which is also why I hesitated in informing anyone while it was going on), but I would expect it to be expensive. I.e. it might ground the plane, at least for a short while. Probably some flames out the back. Maybe it'd even mess up the engine by gumming up the works.
I was never worried for my safety or anyone else's. I know engines are tough, and can eat all manner of crap. And even if they tear themselves apart in the process, they contain it. Not that I'd expect something like that happening at low power anyway.
But really: I don't know for sure what would happen. I'm not a pilot or mechanic, just a nerd with a nerd's interest in engines and airplanes.
Edit: Checking the airline's website, it seems the engine would be a CFM 56-7B26, if that's at all relevant.