They come from beds, mostly. You'll wake up morning and have them filled, sleeping next to you, or just under, sprawled out on the floor like they unrolled from the cot. They are men. Just like you and men, they look exactly as people- but they are all men.
These men act and look as people do. They need food, water, and shelter. They will offer to work at first, but will resort to begging if they have to. They also have desires beyond these needs; they will want luxury, homes, wives, children, and a place in the world.
Every day, there are more of them. They keep appearing, beyond the capacity of where you live. With each, there is less room to move. Your streets are crowded now; and with these men, all available masters are filled with apprentices. All market stalls are fulled staffed- there is no room for your hands. The price of food and drink increases as these men come from every corner, multiplying by the day.
Their bodies are filled with rose water. They look like you and me, but aren't the same. They feel fake, less real, less worthy. They still scream like men do, and beg and plead for their worthless lives, but they only take. Even if they don't mean to; by simply being here, they are a terrible burden.
You could let them stay; but by doing so, lower the quality of life of your own people. Significantly, your country is more polluted and poor. You could also drive them back, but there is nowhere to go. The only "real" solution then is to take upon the task of slaughtering them all, which perhaps will stem the tide, or slaughter them all and stop the problem for good- but it is messy and horrible. They don't want to die, it is a drain on the soul to do this, and others will profit on their misery. They will use it to paint you as a tyrant, or a murderer, for defending what you have. But you aren't defending against an enemy who wishes to kill you- it is a soft invader. But an invader nonetheless.
The truth solution to the Plague of Men? Not all problems have a cure or easy solution; any way you go forward you lose. There is no solution to the Plague of Men.