What makes you think that immigrants don't participate in the economy? Jobs aren't a zero sum game.

When someone gets a job they don't just take your job and then you don't have one. They now have a job and money to spend in the economy. They start businesses and patronize other businesses.

A productive working immigrant is an asset. You are thinking about this backwards: when someone like that immigrates to your country, wealth is being transferred from the home country to yours.