Martha Hollister is an unseen but frequently mentioned character in the Red Dwarf universe.
Martha's husband, Frank Hollister, was the captain of the JMC mining spaceship Red Dwarf during it's ill-fated final voyage, when a radiation leak killed her husband and the rest of the crew of Red Dwarf. (Pilot episode)
The radiation leak killed Frank, but Martha's location during the disaster is unknown, meaning that her ultimate fate is also unknown. Dialogue would imply that Martha was not a crewmember of Red Dwarf, and was not on board at the time of the disaster.
Since Hollister's last residence before joining the JMC was on Phobos, it is possible that Martha lived there or was based there too.
Once, Rimmer, during an argument with Captain Hollister in the captain's office and under the influence of Titan Mushrooms, lost his temper and ate a photograph of Martha, claiming it was a publicity shot for Planet of the Apes that was showing in the cinema. Rimmer ended up with 8 weeks Punishment Detail for this. ("Stasis Leak", Series II)
Three million years later, the crew were resurrected by the nanobots. Rimmer gained access to the crew's confidential files from the wreckage of a Starbug from the earlier Red Dwarf, and used them to try impress the captain. One of the consequences of this was that Rimmer made the captain some blueberry muffins - just like Martha used to make. It worked, making the captain nostalgic and pensive, and the captain invited Rimmer to a captain's dinner. ("Back in the Red: Part II", Series VIII)
Whilst on probation from The Tank, Rimmer waited on a sick captain Hollister. When Talia Garrett entered the captain's quarters, and Rimmer presumed that they were having an affair, Rimmer sarcastically offered to turn the photograph of Martha over facing away from him. ("Only the Good...", Series VIII)