Hi
Is it possible that William could have died by 1901? 
Here is a possible for the family, although Eliza's age is a little out, but closest I could find. See what you think anyway. 
RG13/3432  Folio 120  Page 30
87 Jacob Street, Toxteth Park 
Eliza Cross Head Wid 40; born Liverpool, Lancs
Charles Cross Son 8; born Liverpool, Lancs 
William Cross Son 7; born Liverpool, Lancs 
Thomas P Saunders Boarder Wid 56 - Traveller Commercial; born Carmenthshire, Wales
Regards 
Steve