Big operators self insure up to certain levels
Small operators farm out some maintenance and/or insure at lower levels.
Most crossover points have to do with source of damage as well.
Some FOD is argued as engine generated and versa-visa.
Inlet cowls have often been covered as above the self insurred level. for some operators.
Even the biggest operators often insure for reverser and/or pylon involvement in engine damage incidents.
the fine print rules and subjective judgments are sought