My mother and her younger brother were not registered until they had been discovered (when her brother died). My grandmother was what we'd probably call a Bohemian/Trustafarian, particularly as she'd run off with the stable hand.
She was refused a passport on the grounds that the numbering on her birth certificate doesn't match her age (they changed format in the intervening period). Never had one, missed out on a chance to emigrate, can't provide proof of ID, etc. She was challenged repeatedly by the NHS from the 1950s onwards when needing treatment because the numbers/details didn't match.
It didn't help that she is naturally olive skinned and at the time, had long, thick, black hair. Her one advantage in this time is that whilst she is still olive skinned, her hair is now white, so nobody asks anymore - had she been a couple of shades darker, the 'hostile environment' would have caused her a whole load of bother. She never goes to hospital in the summer even now she's in her 80s because a suntan makes her look foreign enough to be asked for proof of NHS entitlement.
It took months for my passport to be approved as an adult and I repeatedly failed job security checks prior to that point, as I suspect her details caused problems on each application.
Whilst this has been inconvenient for me - and I am just glad I applied and got the passport sorted out prior to the outgoing PM being in charge of the Home Office - I mainly wonder whether her brother could have been treated/not died had his existence been known at the time and hadn't been kept secret. He had a diaphragmatic hernia and, until the PM results came through, her parents were suspected of murder.
Anything could happen to a child kept off the radar - abuse, serious illness, injury, trafficking, murder - and even detention in an immigration facility/refusal of medical treatment later in life.