I'm surprised to run search on the page and find no mention of Mexico, Mexican, or bracero. Part of the reason the bracero program came into being had to do with immigration - people were able to come work then go back to Mexico during and after the WWII years (but many farmers ripped off employees). After that program ended migrant workers came and went for years, but they ended up staying (without papers) because it became too difficult to cross back and forth at the border. They choose to stay for the income from picking up and down the west coast (or the east).

Bracero by Phil Ochs.

I Pity the Poor Immigrant sung by Joan Baez (by Bob Dylan)

As we know, songs morph over time, and while many English speakers know of the Cruel Mother (who took her penknife, keen and sharp. . . ) there is a Mexican song called La Llorona about a Weeping Woman that has a similar theme. In 2015-16 when Syrian exiles tried to reach European countries an encampment formed in Calais as some of them tried to get to the UK. A group of musicians in the camp got together to share and practice and eventually were recorded for a fundraiser, sold as "The Calais Sessions". La Llorona was one of the songs they chose for the story of her sad wandering and it became a sort of anthem of the time. It is a beautiful song.

(I will also note that anything that uses the term "wetback" is probably not a lovely or charming song about immigration or refugees.)