Much depends on what the lease says about insolvency of the tenant. I believe the local authority still owns the freehold of the site, and they want to keep it as an airport.
Normally, anybody purchasing the assets from insolvency would be bound by the restrictions on the original lease.
Shoreham closing would be a disaster for the private piots based there because there would be nowhere else to go. Lydd is great but is a 2hrs' drive, Goodwood is no good (too tight), and that's about it south of London. The aerobatic owners could disperse to farm strips around Sussex OK. Closure would mean the end of training within a huge area; the schools have nowhere else to go.
However, Erinaceous is a long way from actually going bust.