Serious question about immigration & the economy

With the recent Immigrant's Day to bring attention all to the positive aspects that immigrants provide to our economy, I have a sincere question. Obviously, anyone with intelligence would agree that our economy is strengthened with the presence of all immigrants regardless of legal status. I assume that the vast majority of people that emigrate to the US to work are some of the hardest working and most industrious.

Wouldn't that also mean that the economies of their countries of origin are therefore weakened by them leaving?