Slavery is still practiced throughout the world... and, no, there really isn't a way to stop it. You can pass laws to make slavery illegal, but those wealthy enough to have slaves openly are often more powerful or influential than the legal authorities or live in areas where there are no laws against slavery.
Depending on your definition of slavery, you could say that the entire nation of North Korea is enslaved to the government. Traditional slavery still exists in many parts of Africa, where "excess" children from poor families are sold/given to local priests or chiefs in exchange for blessings, favors, money, other goods, even forgiveness of debts or curses. There is a trickle of the ancient Arabic slave route taking Africans north to Muslim nations. And, slavery was a particular concern in Sudan, where a large number of Christian South Sudanese were taken north to serve as slaves in Muslim households. However, a recent peace treaty has given independence to South Sudan. In Asia, immigrants from poor households are often enticed to another nation with a promise of a good-paying job only to find themselves enslaved in a sweatshop factory. The governments in all these cases often overlook the enslaved and support the slavers.
In Europe and the United States, the major form of slavery is sex slavery, although there are sweatshops that exist in both Europe and the United States.
Will speak to the United States... Many young women find themselves in sexual slavery in the United States. For instance, most massage parlors that advertise "Oriental massage" are, in fact, brothels. And the vast majority of the women serving the men in these brothels are de facto slaves.
This is what happens...
A young woman in a rural area of Korea, say, is approached by recruiters and told how beautiful she is. They build her up and promise her that she can be a model in the United States. She is then smuggled into the United States. If she has identification -- particularly a passport -- the smugglers take it away from her. Once in the United States, she is frequently beaten and raped and hooked on drugs. She is also told that she owes the smugglers tens of thousands of dollars for the privilege of coming the United States and is told that she will have to prostitute herself to earn that money back.
She has no identification. She does not know anyone. By now, she may be, and probably is, drug addicted, since drugs are inexpensive to the slavers and give them another layer of control. She does not speak English. She is engaged in something (prostitution) that she knows is illegal and is told that not only will she be arrested if she goes to the authorities, but they will not believe her -- and often that is exactly what will happen. She is told that if she goes to the authorities that nothing will happen to the slavers, but that she will be deported back to her native country where the gang that recruited her will severely punish her and her family. And, if she does go to the authorities, there is a very good chance that the US will deport here to her home where the gang will be waiting for her. She often comes from a very conservative family where prostitution -- even forced prostitution -- would being considerable shame to the family. So she often does not want to go home and explain what happened to her to disapproving family and friends. And other than the ability to lay naked on her back with a man on top of her, and a few skills relating to that, she has no skills. She can't type. She can't use a computer. She isn't a nurse. She lives either in the brothel, or in a crowded apartment where she is taken to the brothel when it opens in the morning and from the brothel after it closes and is cleaned at night. Where is she going to go or do if she gets out of brothel?
And, so, despite being a slave and essentially being raped by every man she sees, for she can't say no to sex, she smiles when her next client enters her room and she does her best to service him. And if he did not go to the brothel, she would not be a sex slave since there would be no profit for the slavers.
These "massage parlors" are found nationwide in the United States. Police rarely check them and rarely run stings to prove prostitution. And, if they do bust the place, the slavers are often cited and released and the girls are handed over to immigration authorities for deportation. The slavers go a few hundred miles down the road, get some new girls and reopen. The girls are deported and, since the witnesses are no longer in country, the serious charges against the slavers are dropped.
Because these "massage" parlors operate openly, there are even websites that rate the parlors on the Internet, they can be easily shut down. The U.S. can offer the girls immunity and a Visa in exchange for their testimony and we can imprison the slavers for long terms on kidnapping and slavery charges. But, we don't...