These laws are what govern who, if anyone, is enslaved or emancipated and where, if anywhere, slavery can exist in your country. They are influenced by both internal and external factors.
Since slavery laws function just like any other laws, it is possible for them to change in different ways, but first, we need to mention the basic laws that govern it.
Slavery Abolished: The law that most countries with advanced economies start with. Under this law, slavery is completely illegal and on its passage, any slave pops in the country are immediately emancipated and converted into laborers. If a country with this law comes into possession of the land where slaves are living, said slaves are also immediately emancipated as above.
Slave Trade: This law is meant to represent the kind of widespread chattel slavery practiced in places such as Brazil and Cuba. Under Slave Trade, the children of slaves are born as slaves and new slaves can also be imported from abroad. The gist of it is that slaves can be imported from decentralized countries that practice slavery if the importer has an established Interest in the region.
Debt Slavery: This law is meant to represent traditional systems of generally debt-based slavery, present in a number of economically less advanced and/or decentralized countries. Under Debt Slavery, Pops of low Wealth levels will gradually create a trickle of new slaves, with poorer pops converting into slaves at a higher rate, as individuals sell themselves or others into slavery for economic reasons such as debt repayment. However, under this system, children born to slaves are born free, so slave populations will not grow by themselves.
Legacy Slavery: This law is meant to represent countries that have made the slave trade illegal but not abolished it altogether, most notably the United States of America. Under Legacy Slavery, the country is divided into the Free States and the Slave States. In the Free States, slavery is illegal and everything functions exactly as if the country had the Slavery Abolished law, while Slave States function as though they had the Slave Trade law with the notable exception that new slaves cannot be imported from abroad. Under this law, slaves also tend to have a slightly higher standard of living for the simple reason that a starving slave population isn’t demographically sustainable.
Trade may follow the US example and change to Legacy Slavery as a compromise alternative to abolishing it altogether, and a country that has fully abolished slavery can even try to bring it back. Given that no country in history actually re-legalized chattel slavery after abolishing it, this is very difficult to do, once abolished there will generally be a strong anti-slavery bastion in a country that aren’t going to look kindly on such proposals. Of course, trying to abolish slavery isn’t likely to happen without resistance either - those wealthy aristocrats who benefit from it have a vested interest in defending it, after all.