There have been changes in the county boundary in the Markyate area which could affect whether events are recorded in Hertfordshire or Bedfordshire and whether the relevant parish is Caddington, Flamstead, or Studham - see www.hertfordshire-genealogy.co.uk/links/markyate.htm
Are you sure that the 81 year old Mary Cain listed in the 1861 cenus as being born at Clifton, Bedfordshire, is the same Mary Cain who was 71 years old and was said to be born at Flamstead, Hertfordshire, in the 1851 census? (See www.hertfordshire-genealogy.co.uk/links/right-name.htm
for the dangers of jumping to conclusions)
A Mary Cain death was registered in Luton in Oct-Dec 1860 (3b 254) and another in Oct-Dec 1864 (3b 311) but unfortunately the age is not indicated in the index in either case so you would need to buy the death certificates to find out which, of either of them, is her.
A complete wild idea - The was a baptism in Caddington, Beds, in 1781 with the strange Mary Amias - could this be a transcription error - and if so for what. Vass is one of the possibilities and Eames is another. The only way to sort this out is to look at the original handwriting in the register (on microfilm). Of course if Mary was born into a non-conformist family there may be no record of her birth/baptism.