Is obtaining an unemployment benefit while working in the private sector without social security, and pledging that there is no private work, and obtaining an unemployment certificate with two witnesses, considered lying and deception?

If the grant is conditional on not having a private job and requires certification of that, then it is not permissible to apply for it while having a private job. This is based on Allah's saying: "O you who have believed, fulfill [all] contracts," and the Prophet's (peace and blessings be upon him) saying: "Muslims are bound by their conditions." The fact that the state will not provide a job if one does not register for the grant is not an excuse for lying, cheating, and violating the condition.