Employment history on such a document is likely intended to simply show that you have a history of employment. Depending on the situation, it is probably unlikely that past employers would be contacted (unless the application involves permission to work, and then it may be more likely).
A private company is unlikely to have the ability to determine with absolute certainty that you worked at XYZ Business for five years, but a foreign state may have the ability through treaties to gain access to tax or other records from your home country that would, in fact, show you paid taxes on income from that company.
It is also likely the application has a bit near the signature section about you attesting to the truthfulness of the document. Signing a document you know to be false is almost certainly (definitely?) universally illegal.