I never closed a site but been part of buy out eg buying the site that closing down, in terms of license etc IPS advise not to give over details but to transfer license over to new account, not sure if this still case but one ticket to staff would solve.
As for data if sold off this is new tricky part many customers might not like there data transfer to new owner but then again might like it if the site active and busy, as for archive the site what does this solve ? Still need keep hosting and domain paid so buying for site that will sooner later drop off google ranks.
You need look at why are closing the site question is because visitor numbers and posts stopped? If so why ! Is because another site better ? Or social media replacing the market ?