I don't know Shoreham but a number of general principles apply here.
First, the job of an administrator is to try and salvage the company but also to obtain maximum value for creditors. This will usually involve disposing of the valuable assets as going concerns.
The BBC report says there are 30 businesses at the airport. Many of those will have leases, which give the tenants a number of projections. One of the most important is that the landlord (usually the freeholder) cannot "derrogate from the grant" of the lease. This means that if you as a landlord grant a lease for say a flying school or aircraft maintenance facility, there is a clear implication that the business will need the use of an operating airfield! Fairly obvious really. However, the landlord cannot then turn around and remove that facility.That is a breach of an implied term in the lease. I suspect that a similar argument may have been used at Lee on Solent.
So, whoever buys the airport will take it subject to the leases held by the businesses and the right to use the airfield. Most of those leases will also offer the tenants substantial protection from eviction and entitle them to a new lease at the end of their existing terms.
As for anyone with an aircraft there, I cannot see there would be anything unlawful about removing their aircraft by flying them out. They could not of course bring them back without consent from the administrator. This is so even if they do owe money, unless the airport has already exercised a lien over the aircraft.