The freehold of the airport is owned by the local authority.
Erinaceous had a long lease on it, with a requirement to maintain aviation activities (don't know the exact wording) for some 25-30 years.
If Erinaceous go bust then the answer depends on the terms of the lease.
With some leases, the asset will revert to the freeholder. (which would be really funny in this case since AIUI the council got the deficit paid off in the sale and now they would get the airport back free of the deficit)
With most leases, the asset is at the disposal of the receiver or the liquidator, but they are still bound by any restrictions in the lease. Anybody who takes on the lease will also be bound by the same restrictions.
In the short term (years) I don't see Shoreham closing. In the long term, the property sharks will get all possible land and that will be the effective end of UK GA... another 20-30 years I reckon. Only farm strips, and expensive places like Bournemouth & Norwich etc will survive. Unless planning law is changed to create a development presumption enabling the development of airfields in open countryside.