Once upon a time,
On a flight line long ago,
An ordnance man held up the safety pins he had just removed from the missile pylons,
And they were promptly sucked out of his hand and down the engine inlet
by the attached fabric streamers.
I had a chance to observe the resulting damage to the engine blading following engine removal.
By far the worst damage was done by the fabric streamers as they caused the blades to untwist as they interfered between rotor and stator blades.
A dissassembled container frequently will contain fabric components, and there is nothing to stop those fabric components from following the airflow.
All you can do is hope that it is only the secondary airflow components that catch the bulk of the FOD because if the core engine catches the FOD, there will be really big $$$$ to pay.