Can an addition be permitted but not recorded ( Los Angeles)

[Alvin Uy]

So I went to go look at a 2 Unit (duplex) today thats listed on the MLS. I noticed the square footage on title does not match square footage that I saw. The listing price per square foot includes the addition however. The owners (man and wife in their 70's) say the 2nd Unit (1bd/1ba) was built with permits for their daughter decades ago but was not recorded because owners did not want to pay additional property tax on the build. My realtor did some digging online and found permit of second unit on this property filed with city. I should also mention that the lot is zoned for up to 3 units, so I can still force appreciation by building a 3rd Unit, but would hate to have to tear down the 2nd unit if it wasnt truly permitted. So now im baffled by this and not sure what to offer... is this 2nd unit truly permitted but not recorded on title? I had no idea thats even possible to do.