The way political machines, such as Tammany Hall, work with and for immigrants is by promising bills and laws in favor of immigrants in exchange for votes.
Political machine, in U.S. politics, is a party organization, headed by a single boss or small autocratic group, that counts on enough votes to maintain political and administrative control of a city, county, or state.
Tammany Hall was a New York City political organization founded in 1786. It was the Democratic Party political machine that played a significant role in controlling New York City and New York State politics and helping immigrants.