BackgroundMarriages in ancient times were different than they are today. They were usually based on written contracts that both families agreed to before the marriage took place. The most common Roman marriage contract was called "Conventio in Manum" and it made the wife subject to the husband. This is most likely the type of marriages that Paul was dealing with in Ephesus. We no longer have written contracts in marriages today and so Paul's words no longer apply to marriages in that respect.
In the case of those at Ephesus, the wives were not honoring the marriage contracts fully because of a false teaching regarding Lordship. The wives considered Christ Lord over them instead of their husbands in some areas of their marriage.
BackgroundPaul is addressing the same type of issue regarding slaves. In the ancient world, most slaves would have sold themselves into slavery to pay off a debt that they could not pay. There were no credit bureaus in those days and no central banks to promote debt. Rather, one worked to maintain a good reputation so that people would trust them. If one were to break their word and not repay a debt, it would be difficult to operate in a honor/shame culture. Additionally, if one could not repay their debt, they could be thrown into a debtors prison. Selling oneself into slavery was preferable to the other consequences. God takes steps in the Old Testament Law to keep that from happening to any Israelite. He prohibits Israelites from collecting interest from other Israelites (Deuteronomy 23:19). Every Israelite family had a land inheritance that they could sell as a last resort to get them out of debt (Numbers 26). Finally, every seven years, all debts were cancelled (Deuteronomy 15:1).
When someone sold themselves into slavery, there would have been a contract that would, among other things, determine how long they were to be a slave. There was a false teaching regarding Lordship that was causing the slaves to not submit in some cases. In other words, this false teaching was causing slaves to disregard their earthly masters because Christ was their master. Again, they were not disregarding their earthly masters in all areas of their authority, only certain areas as specified in the false teachings. God does not want His people to be in slavery but He does want them to keep their word.