Funnily enough I actually have been thinking about that part recently and ironing out the details. A very important plot-point reveal is that Eugene, i.e. "Dad", was an abduction case in the rural Rust Belt part of Wisconsin that was never solved. I don't think he ever left the house for the first few years and when he was allowed to leave it was strictly monitored and controlled, but for the most part it's like he materialized out of thin air sometime in the mid 1970s.

When his captor suddenly keeled over of a heart attack in 1971, 18 year old Eugene discovered documents revealing that the man had an older brother who died years earlier, leaving behind a son who had been estranged from the family and largely out of contact for over a decade. Seizing the opportunity he forged a simple will in which the captor leaves the house and land to "my beloved nephew, Eugene Johnson." With almost no living relatives, minimal estate value, and the captors well-known reputation as a reclusive eccentric, the will was able to pass through informal probate with very little official scrutiny. Eugene then steps into the dead nephews identity, using the his existing birth certificate and any other scattered documents he finds in the house. In the pre-digital age it's practically fool-proof. Since then he has been gliding by on savings and the little income he brings in through telemarketing, an easy job for someone who doesn't enjoy leaving their house much.