OP, you have to assume that they will contact all your previous employers, and they will undoubtedly call a) all previous aviation employers and b) the most recent 1-3 jobs you have had (depending on duration).

Don't leave anything out. If the company is out of business, say so. If you got paid cash under the table, don't worry about it. You can get cash under the table and still have a reputation for being a hard worker. They won't check tax returns.