Sometimes they simple left a suitcase at an address just to claim they were living there. People were taken at their word, nobody checked the information was correct, especially in highly populated places. It is the same with stating their status as widowed on remarriage. It was very easy to be economical with the truth.
I remember coming across a couple who separated and the husband simply remarried as a widower and set up home with the new with the “new” wife in the next street to where his legal wife was living.