Recruitment will be a big challenge
Global international migration (people moving to a country different from a country of their birth) in 2019 was 272 million people or 3.5% of the global population. Two thirds (2/3) are labour migrants (people who move to another country because of their jobs). The main migration patterns are related to the economy: People move from less developed countries to more developed countries. However, most international migrants move between countries within the same region.
Despite what other answers say, recruitment will be a challenge. People do not move to another country randomly or on a whim. They do it chiefly for 2 reasons: 1) The destination country offers concrete opportunities (an existing and confirmed job offer, existing support networks [family, religious, ethnic, and similar networks]); 2) It is no longer possible for them to reside in their own country due to war, famine, etc. (still most people will not move far).
Personal motivations of migrants are a complex topic outside the scope of this question. I just want to mention that there is no consensus when it comes to migrants. A lot depends on countries of origin and destination, history of migration for both countries, family situation, reasons for migration, and so on.
You also need to consider that migration is not a personal decision, but rather a household or family decision. When you recruit people for your experiment, you need to convince all people in the household, not just one person. Moreover, this is not limited to nuclear families. Extended families (grandparents, uncles and aunts, etc.) will often have a say as well, especially in cultures with traditions of filial piety.
Please also note that it is rather rare for the poorest strata of society to migrate. Poor people cannot afford to move to another country and do not have the necessary social and economic connections.
Your recruitment strategy should focus on:
- offering people security if they move (since this particular country is a lawless country where every man for himself, you should offer benefits for those who are left behind, e.g. monthly payments to the family, educational and job opportunities for children);
- recruiting 'villages' instead of individuals (you need a lot of people, so offer to move entire communities instead of people, you have to promise that you will keep them together [whether you stick to it or not is up to you, but if you don't make sure that no one knows about it]);
- use targeted advertisement strategies (hire someone like Cambridge Analytica that can target small segments of the population with messages tailored to their preferences; it will also save you some money);
- paid relocation expenses (all expenses should be covered by you, this will make it possible to recruit the poorest people);
- simple procedures (all immigration procedures should be very simple, so people with low educational levels or people with low attention span are not disadvantaged; again, you need to recruit a lot of people and people do not like to move, so you cannot be choosy);
- allow families to migrate and stay together (if you limit immigration only to persons of age above 18 you will miss a lot of family men and women who refuse to leave their children behind);
- you have to be extremely careful when informing people that they are a part of the social experiment (no one likes to be a guinea pig; it is better not to tell them at all but if you must you might want to mislead them to avoid compromising your research data).
With this said, I seriously doubt that you will be able to find 50 million people who will voluntary move to a lawless country where they can be killed on sight for no good reason. Self-preservation is a strong biological imperative. Most people will avoid placing themselves in situations where they can suffer harm for no reason.
What you can expect is a quick formation of law and order in your country. People will form alliances to protect themselves and establish rules. And they will start doing it even before they board whatever is used for transport.
If you try to enforce lawlessness people will band together against you. It would also not be unexpected if your country population develops hostility toward experimenters if their involvement is not limited to discreet observation (which means no cameras). You can check the history of space flights and research in isolated environments to see how relationships between crews and remote control centres can deteriorate.