What is the Spanish word haiga? Is it a properly conjugated form of a verb? Or a regional variant or improper conjugation? Where/when is it used?
It is a regional variant of "haya" (first and third singular person, subjunctive present of the verb "haber"). You will hear that word from some people with low education in a natural manner, and also from well-educated people in an informal conversation, either trying to make a joke or just put emphasis on the word by pronouncing it incorrectly (especially when "haiga" is pronounced slowly).
If you find that word in a written document, it will probably be part of a dialogue, in which case you should probably assume that the character is not well educated.
According to the dictionary, "haiga" it is also a noun, an informal word for a big, ostentatious car. However, this is the first time I hear about that meaning, and I'm a native speaker of Spanish. Maybe it's just a local word in some country, and this origin might be irrelevant since the word is not used very much (that, according to the diccionary as well).