Abigail Pettigrew

Abigail Pettigrew was one of the people taken by Elliot Sardick as "security". She developed a romantic attachment to his son, Kazran, due to alterations made to the timeline by the Eleventh Doctor.

Frozen
Abigail was cryogenically frozen by Elliot Sardick against a loan of 4,500 gideons to her family. This sort of "security" allowed him power over those who owed him money. Abigail suffered from a fatal disease; the freezing prevented her death but when she awoke her condition deteriorated again. A counter placed on the outside of her freezing chamber kept count of the time she had left to live if unfrozen. (TV: A Christmas Carol)

Original timeline
In the original timeline, Abigail remained locked in her ice box without ever being released. When her sister was elderly, she and her family approached Kazran Sardick to release Abigail to just spend Christmas with them. However, Kazran cruelly rejected the family's pleas as they could not pay any of the debt that Abigail was collateral for. When the Eleventh Doctor arrived to get Kazran's help in saving a crashing spaceship, he spotted Abigail whom Kazran dismissed as being no one important. As Abigail was taken away, the Doctor commented that in all of his long life, he'd never met a single person who was unimportant. (TV: A Christmas Carol)

After Kazran's timeline was changed
When the Eleventh Doctor went back in time to alter the course of Kazran's entire timeline, Kazran and Abigail first met after Abigail was awoken by a twelve-year-old Kazran and the Doctor. She was able to calm a sky shark hunting them by singing to it. She went with them in the TARDIS to return the shark to the cloud belt. 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. In the changed timeline, Abigail was allowed out so she could have an early Christmas dinner with her family on one Christmas Eve. She went on trips in time and space with the Doctor and Kazran for as long as she could, but when she only had one day left to live unfrozen, she told only Kazran of her illness. She returned to her case. A thoroughly heartbroken Kazran told the Doctor only that he did not want him to return next year as the annual outings had gotten "old".

Many years passed and Abigail remained frozen. A spacecraft was damaged in the cloud belt 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. (TV: A Christmas Carol)

Personality
Abigail had a sweet, affectionate and kind-hearted personality. A holographic recording on her ice chamber pictured her thanking Elliot Sardick for his generosity. She was an extremely good singer and was able to easily calm even the sky sharks. Abigail became increasingly attached to Kazran, particularly as he got older, to the point of romance. When he woke her on the last day, she affectionately teased him about waiting so long to release her and chose to spend her last day with him. (TV: 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 and Kazran are in fact the first "one-offs" since Donna Noble in The Runaway Bride to travel through time and space in the TARDIS, fulfilling a generally accepted criterion for being a companion.