I am looking for a (preferably economic or environmental) force/system that would every few months or years force a random sample of the middle/lower class of an area to migrate away. This would be taking place in a mildly dystopian, realistic world set in either current time or within a hundred or so years.

The goal of this is to create groups of people who come together for a short-ish amount of time and are then forced apart. This is seen as quite devastating, but a part of life. Families may only stay together for a few years, spending your whole life with them would be hugely lucky.

My thoughts first go to some sort of seasonal resource gathering, but what stumps me is the necessity that only certain random people from the groups need to go to the new place. It would be no trouble for these people to be in some sort of indentured servitude to massive corporations that force the migration, but what would be the benefit of moving a random group of your workers to a new location when they would know that keeping families together would improve morale and thus productivity?

I appreciate any help in sketching a system where this would be possible

This is already done in the army

In the U.S. Army, they move people from base to base all the time, not because they need more people here or there necessarily, but because they intend to prevent factions from developing within the service due to prolonged proximity. Randomly moving people around all the time homogenizes the military and protects its leaders.

Suppose your fictional nation requires every citizen to be a trained militiaman. Now it's got constant potential for factions to develop within its borders, and those factions would be made of trained/armed militiamen -- it's not desirable.

So, to solve this problem, the national government socializes housing and regularly issues semi-random commands, ordering citizens to move from their current location to a pre-selected destination. Upon receiving such a command, the citizen may apply for an extension to their current post, or they may apply for a specific destination. Also, at the discretion of the government, they can order people to move without bringing family along, but to avoid discord this is much more rare.

A major food source for the people is an insect that has a similar lifecycle to a cidada where each swarm lies dormant for a number of years and emerge all at once to breed. The difference here is that that they do not have a predictable emergence time and they are only out for a few days. The people move to the region they think the next swarm is going to emerge. There are enough swarms around that they only have to wait a few weeks at most for the next one, but if you are not in the region where the swarm emerges, you can't harvest enough of them to make any money. The swarms are plentiful enough that they can feed people, but they are unpredictable enough that they have to move around and can't stay in one area for a long time.

The harvesters are run by people who have proven that they are good at predicting when the swarms emerge and the size of the swarm. They designate the assignments for each harvesting party and it can get pretty arbitrary as to who is assigned.

Differing abilities

Some people are better able to do whatever the task is. But it's hard to tell who until someone actually tries. So there is a constant stream of people being added to the location to attempt it. And a constant stream of people leaving who failed.

Differing sensitivity

Some people have an allergic reaction (or similar) to something in the local environment. It doesn't need to be an immediate reaction. Perhaps it takes even a year to show. But once it shows, it's obvious that person can't stay. Again, assume that the only way to check for it is to actually try to live there.

Instead of indentured servitude, go to the opposite extreme; everyone is an at-will freelance employee in a job-scarce industry controlled by a few corporations. Unemployment is high. If you have a job, you hang on to it and, if you don't, you go wherever the work is. Corporations know that people are desperate for jobs and will travel to get them, so they have no incentive to treat workers fairly. In fact, they know that desperate, isolated people will accept increasingly terrible working conditions, so they deliberately move jobs around in order to destroy the stabilizing institution of the nuclear family. Business is slow in Chicago? Cut 100 jobs there. Things are picking up in Des Moines? Add 50 jobs there. People who lost their job in Chicago will rush to Des Moines, even if their spouse or sibling was one of the lucky ones who didn't lose their job in Chicago; in fact the corporation probably planned it that way, although they might not admit it. The jobs are low-paying, poverty is high so, as soon as a child is old enough to work, they too will separate from the family and go to any place where jobs are available. "Old enough" can be adjusted based on the level of distopia, obviously.

I'm taking some inspiration from The Grapes of Wrath and the Dustbowl era generally. If you haven't read it, I recommend doing so.

One option would be if there was a plant or animal species that had a non-annual boom and bust in population. Some plants, like onions for example, have a biennial life-cycle. Some animals have population booms staggered over longer periods, such as cicadas.

So a social group could form who specialize in harvesting such a crop/species. For example, group X hunt reptilian whales that only approach the shores every third year. They make a great living that year but then need to find other work for the next two seasons, so they disperse and do odd jobs all around the country in the intervening years.

If you are happy with shorter-term seasonal migration, then that still exists to some extent in the real world. For example, in New Zealand, itinerant fruit-pickers often arrive from smaller Pacific Islands in autumn, work for a few months, then emigrate back to their traditional homes etc for winter/spring/summer.

I'm going to take @Willk's controlling AI a step further. Quite a few steps further.

Remember the story (*) of the Christmas Truce from WWI? There were often informal cease-fires on Christmas and Easter, but on one battleground the troops took it to another level. They met up in no-man's land, shared drinks, swapped souvenirs, sang carols together. When the high command heard the story they were shocked -- a hundred years ago warfare depended heavily on seeing the enemy as nearly inhuman (+), and this kind of fraternization could destroy that. The units which participated were disbanded, the troops scattered into dangerous assignments on fronts as far apart as possible.

Our benevolent AI doesn't let things get that far out of hand, of course. But if you share a racist joke with a co-worker and they smile and laugh, you might find your whole company scattered the next week. A group of friends start reinforcing each other's bad habits... scattered. Those cliquish bullying kids at school? Carefully placed into loving supportive environments where they can learn from better examples.

There is enough of a background of actually random movements to homogenize society that the pattern is buried, but it's there. Bad behavior is culled out by forcibly breaking the social networks that support it.

(*) It's quite a story. It might even be true, or partly true, or a romanticized version of the truth... but it's quite a story, in any case. I'm retelling the version from a particular source from memory, and Wikipedia doesn't quite support this version.

(+) See for example "The Germans and Austro-Hungarian soldiers were depicted as inhumane savages" from the Wikipedia article on WWI propaganda.

Could it be economical? Think of an exaggerated version of what is happening these days in some cities (San francisco, Vancouver, etc.)

Structure the tenancy laws in a way that allows for tenants to desert properties whenever they wish, and landlords to price properties as they wish. This is a perfect situation for runaway housing markets.

The tenants

Are poor (middle class). They cannot afford to own property so they must rent. When a new city is formed, some of the upper of the middle class buy properties, and rent to the lower middle class. The lower middle class rent in this new city, with rent being affordable.

As this particular city grows, rent skyrockets (as it legally can) and the upper middle class become the rich. The lower middle class either win and can afford property in another city, to which they abandon the current landlord (as they legally can) to become a landlord of their own. Otherwise, they lose, can't afford rent, and move to rent in a cheaper city.

The landlords

Stem from tenancy, or are the otherwise filthy rich. Some of these landlords may lose during a migration, and end up poor (lower middle class, a tenant), having to try again.
Their goal is as much money as possible, and because of the tenancy laws, competition doesn't really exist. All landlords raise their prices in unison, to suck as much financially from the lower middle class as possible (keep them lower middle class, don't give them a chance to advance).