To leave the country, you need an exit visa which requires the consent of your employer or sponsor.
So, no.
Personally I would never take the risk of taking employment in an autocratic country that requires an exit visa. They could pay me annual seven figures, but it makes no difference because they'd be able to extract whatever they want from me as a condition of departure. Imagine being held in a cell at the Riyadh airport until you wire them all the money in your foreign bank accounts. Nothing at all stops them from doing that.
If you don't believe this could happen to Western expats, read this story about KPMG employees in Saudi Arabia:
'Several former employees suspected they were under some form of surveillance by KPMG Saudi Arabia while working in the kingdom. One says he was followed by a car whenever he left his compound while exit negotiations were ongoing. He says he had safety concerns “every day” during this period “and any time I stepped out of the security of the compound”.
'Another former employee only agreed to speak to the FT from a hotel landline while travelling in Europe in case their mobile phone was being monitored. “As you know we are being watched in Saudi,” the person said.
'A third former employee says that when he finally left Saudi Arabia for good, he deliberately took a circuitous route via Bahrain so as to avoid being tracked or blocked from leaving by the firm or its government contacts. He compared the behaviour of KPMG Saudi Arabia’s leadership and the fear it instils in employees to the John Grisham novel The Firm, a thriller in which a lawyer becomes entangled in a corporate plot. “I was in fear for my own safety,” he says. “I would not have taken my young family to the Middle East had I known. [That fear] just should not exist today.”
Still though, most of those people come to the gulf countries voluntarily. Not that it justifies the abuse, however I presume they are still escaping an environment that's not much better. Or at least the meager allows them to escape it to some degree. What else would expect that new people keep coming to those states?
So it seems a bit better than slavery, more like wage slavery many immigrants to North America faced during the 19th century. Of course the migrants workers in Saudi Arabia and gulf states are certainly aware that they will never will be integrated into the local society unlike the European immigrants.
They made some changes to their kafala system last year that makes it a possibility without needing employer's consent, but under very specific circumstances that don't apply to majority of workers.
For example one of those rules is a full year of employment, but non-skilled workers rarely stay that long to begin with.
Perfect example of doing something that counts as "progress" while not actually changing anything.
