What is the ruling on using government-produced oil from the "public sector" for frying employees' personal food, taking into consideration that they receive a cash meal allowance, and does this fall under the ruling of "those who work with it"?

If the authorized officials of the factory permit the use of the oil for a need, then there is no blame upon the workers within the limits of what they have been explicitly or customarily permitted. However, if they do not permit it, then it is not permissible to benefit from any of it because it is an encroachment upon the property of others. The argument citing the verse: "and those employed to collect the [zakat]" is invalid; this verse is specific to the recipients of zakat and the collectors who gather it.