Getting an exit permit is separate from having your passport. Yes, you do need an export permit under normal circumstances to leave the country. But in "abnormal" circumestances, you need to be able to prove your citizenship/identity. NO GOVERNMENT has the right to take your passport indefinitely. Your passport is the property of the nation that issued it.

It is the practice here in the GCC for many employers to "hold" passports of their employees (illegally). Get yours back ASAP.