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By definition welfare is a net loss. Otherwise it wouldn’t be needed.

How can it be bad for immigrants to get more than they put in, but not citizens?

The “immigrants will get more out of welfare than they put in” is exactly how welfare is supposed to work!

Welfare recipients spend every penny they receive so it contributes to the economy by keeping money moving.

It's not a zero sum game.

Many (most in some countries) immigrants are citizens, so I don't think that's the distinction you meant to make.