Rebecca, status married, born Gretton,can be found in 1861 with Pullette W, born 1858, but no sign of Polite (etc) Villitte, husband (name from marr cert). On the 1871 Census she is a widow, without Pullette W, born 1858. Her relationship to head of household is not given.
So, where is Polite in 1861?. Cannot find a death between 1858-1871.
On the 1861 Census, both Rebecca and her son (my 2 x Great grandfather) Pullette William Villette are living with Rebecca's brother John Hull in Gretton, Northamptonshire.
Then, like you, when I looked at the 1871 Census I realised Rebecca was no longer living with them. (Pullette) William Villette is still living with his uncle John Hull in Gretton but Rebecca seems to have left the household.
This kind of fits in with some details I was given by another poster in the original thread. They posted some info they'd found that, in 1866, Rebecca was in London (Marylebone) with her baby daughter Rebecca in a workhouse - both were said to be "ill" and the baby died on 11 August 1866. There was a note with this record saying that Rebecca's husband (Polette, of course) had left her 8 months prior to this.
By the way, on the 1861 Census when both Rebecca and her son (Pullette) William Villette are in Gretton, there is no Polette Villette (Rebecca's husband).
So my picture so far from the info we currently have, obtained through helpful posters on the original thread:
Polette Villette marries Rebecca Hull on 18 May 1858 in St James, Westminster. The witnesses to marriage are, I think (?), Charles Villette (Polette's father) and an Amy Villette.
Polette and Rebecca Villette have a son, Polette/Pullette/Pullit William Villette (whom I will from now on just refer to as "William Villette") who is baptised at St Anne's in Soho in February 1859.
In 1861 Rebecca and son William Villette have moved from London to live with Rebecca's brother John Hull in the village of Gretton, in Northamptonshire. Polette Villette doesn't seem to have made the move to Gretton with them.
In July 1866, there is a record of Rebecca having been admitted into a workhouse in Marylebone, London - she is sick with a newborn baby (also called Rebecca) who dies on 11 August 1866. Notes on this record say her husband, Polette, had left her 8 months prior.
In 1871, William Villette is still living with his uncle in Gretton - but Rebecca is no longer living with them. I would guess, sometime between the 1861 Census and the Marylebone Workhouse record of 1866, Rebecca must have moved from Gretton back to London (to be back with Polette?). The couple split up/Polette leaves her while she is pregnant (8 months prior to July 1866 would be December 1865, maybe he left her when he found out she was pregnant).
Polette Villette then dies some time before the 1871 Census - because on that Census Rebecca is described as being a widow. Or, perhaps, he has simply left Rebecca and she does not know his whereabouts, and she just tells the person/people doing the Census that he is dead.
My strongest hunch is that Polette Villette was from France, came over here to the UK for a very short while (just a few years) where he married Rebecca Hull who gave birth to my great-great grandfather William Villette in 1859 (some online records say 1858) and a daughter Rebecca in 1866 who died as a baby. Polette left Rebecca pregnant with daughter and possibly went back to France? His possibly having been born in and going back to and later dying in France, is why we have no British records of either his birth or death. This is my theory.
What do you think?