The downturn in the world economy is REAL. If BA goes into receivership, the employees won't get ANY checks for a while. Then they'll start getting them again, but they'll be for a lot less. They may look back at the times when they were only being asked to work "one month for free" as being the Halcyon Days of their company, and of their carreers.
If I were in their shoes, I'd seriously consider the offer.