Having financial security

They are not filthy rich, but are well-to-do/// Non sono ricchissimi, ma stanno bene

They started from scratch, with no money to spare, but now they are finally quite well off

Hanno cominciato dal niente, senza tanti soldi, ma oggi finalmente se la passano bene

This phrase may be a shortening of come well off, that is, "emerge in good circumstances". (First half of 1600s). (Christine Ammer; The American Heritage of American idioms)