I found a mother and child who "vanished" when the son was very young. Fortunately I had the son's two Christian names, and the mother's first name, and both came from the same small place in Wales. After a LOT of searching, and with wonderful help from a now departed researcher, we found the pair with a new male, under the very original name of "Smith" in another part of the country. We couldn't find Mr Smith before then, either.
Long story cut short, they seem to have gone off with him, he left his wife and family, and they stayed together until his death. The together had another child, and after "Mr Smith" died, when he reverted to his original surname, which his younger son adopted..... and his "wife"s older child, the actual relative I was seeking, resumed an alternation between his mother's original surname, and the surname of her original partner, almost for the rest of his life. (We've never been able to find an actual marriage between his Mum and that partner ).
It happens!
It's marvellous what you manage to find them and prove it, though.
Took us years, but it shows - never give up!