Such undesirables include traitors, would-be tyrants, and individuals who were enemies of Rome, according to Harriet I. Flowers. This posthumous dishonor was considered the worst that could be done to a former senator. Here's an example from Tacitus of what was done to condemn the memory of Piso:
Cotta proposed that the name of Piso should be erased from the records, one half of his property confiscated, and the other made over to his son Gnaeus, who should change his first name; that Marcus Piso should be stripped of his senatorial rank, and relegated for a period of ten years....
Tacitus Annals 3.17
Acts subsumed under the rubric of "damnatio memoriae" include scratching names and titles from inscriptions, defacing likenesses, banning the condemneds' wax masks from funerals, confiscation and destruction of the condemned man or woman's writing, annulling of wills, marking the birthday of the condemned as a day of ill-omen, marking the anniversary of the condemned's death with thanksgiving, mutilation of corpses, and more. The condemnations could be started by the Senate, the emperor, or the army.
Women as well as men could suffer, but the causes were not the same. Women could be condemned along with their men (husbands, fathers, or brothers) or because of controversy with the emperors. Eric R. Varner lists the imperial women who suffered some form of damnatio memoriae: Julia Maior, Julia Minor, Agrippina Maior, Claudia Livilla, Milonia Caesonia, Valeria Messalina, Julia Livilla, Domitia Lepida, Agrippina Minor, Claudia Octavia, Poppaea, Antonia Claudia, Lucilla, Crispina, Annia Fundania Faustina, Plautilla, Julia Soemias, Otacilia Severa, Cornelia Supera, Magnia Urbica, Galeria Valeria Maximilla, Prisca, Galeria Valeria, and Fausta. See Emperors Whose Memories Were Erased.
References:
- "Rethinking 'Damnatio Memoriae': The Case of Cn. Calpurnius Piso Pater in AD 20," by Harriet I. Flower Source: Classical Antiquity, Vol. 17, No. 2 (Oct., 1998), pp. 155-187.
- "Portraits, Plots, and Politics: 'Damnatio memoriae' and the Images of Imperial Women," by Eric R. Varner. Memoirs of the American Academy in Rome, Vol. 46 (2001), pp. 41-93.
Photo of Arco degli Argentarii - Internal side - Caracalla and figure scratched out
CC Flickr User Panairjdde

Comments
So these campaigns of DM were not always 100% successful? Last October at the Uffizi Gallery, I saw several of these ‘non’ people in statuary form.
I am interested in now looking up how damnatio memoriae relates to the term Giorgio Agamben talks about in his book by the same title Homo Sacer. It may also be interesting to consider how close the many exiles, such as Ovid and Seneca, came to being treated in this way rather than “just” being exiled and having their propery taken.