Abigail Pettigrew

Abigail Pettigrew, the sister of Isabella, was one of the people taken by Elliot Sardick as "security".

Frozen
Abigail was taken by Elliot Sardick and cryogenically frozen as part of a loan of thirty-five hundred guineas to her family. This sort of 'security' allowed him to barter with those who owed him money. Abigail suffered from a fatal disease; the freezing prevented her death but when she awoke her condition deteriorated again.

Christmas adventures
Abigail was awoken by Kazran Sardick and the Eleventh Doctor. She was able to calm a sky shark that was hunting them by singing to it. She went with them when they returned the shark to the cloud bank. Abigail then returned to her case. Just before she froze Kazran promised they would visit each year.

Kazran and the Doctor woke her every Christmas Eve and took her places. Over the years as he grew older, she and Kazran fell in love.

When it came to pass that she had one day left to live unfrozen, she told Kazran of her illness. She returned to her case. Kazran told the Doctor not to return next year as the annual outings had gotten "old".

Final day
Many years passed and Abigail remained frozen. A spacecraft became damaged in the cloud bank on Christmas day, and was about to crash. The Doctor needed Abigail to sing, which would break up the cloud and allow a landing. Kazran was reluctant; he had been unable to choose what day should be their last together. Having awoken and heard the question, Abigail exited the stasis pod and told him "Christmas day".

She sang into the Doctor's sonic screwdriver. This was transmitted to its other half in the shark. The cloud opened and the ship survived. Kazran and Abigail spent her last day together, using the shark to fly across the sky in a carriage as they had in one of their first adventures with the Doctor. (DW: A Christmas Carol)

Behind the scenes

 * Unlike other one-off characters appearing in recent specials, Abigail was never promoted by the BBC as being a "companion" of the Doctor. Ironically, however, she (along with Kazran) are in fact the first "one-offs" since Donna Noble in DW: The Runaway Bride to travel through time and space in the TARDIS, fulfilling a generally accepted criteria for being a companion. (Wilfred Mott is a special case as he had already been an established supporting character in numerous episodes before his companion status was affirmed in DW: The End of Time.)
 * It is possible, although profoundly unlikely, that Abigail's surname is a reference to Peter Pettigrew (A.K.A. Wormtail) from the Harry Potter series. Elliot and Kazran Sardick are both played by Michael Gambon, who plays Albus Dumbledore from the film version Prisoner of Azkaban onwards.