A Suicide Villain is someone who decides to be a villain for the purpose of getting killed.
This is different from an already-established villain who chooses to kill themselves or let themselves be killed rather than to face prison. This is someone who becomes a villain for the sole purpose of being killed.
Otherwise known as "suicide by cop" or "suicide by hero", the process of being a "suicide villain" is not a spur-of-the-moment activity. Great planning is put into crafting a villain persona to identify as someone who needs to be "taken down".
The catch is that this is not done to benefit the perpetrator, but rather to cause damage to the person they are goading into killing them. This is done to damage their reputation or to force them to violate their moral code against killing.
This is similar to the Kamikaze pilots of Japan during World War II, whose dedication to their country and their emperor were such that they willingly killed themselves to cause damage to their enemies.
At the time, Galatea Future had just won her legal independence from the copyright claims set by Markman Gold. The former heroes, all suffering from stage-4 cancer, targeted Galatea Future because they believed that her "freedom" would be short-lived in the courts. By discrediting her as a hero, it would supposedly harm her worth to Gold, and thus hurt him. While the theory was questionable, the use of former heroes as suicide villains were real and they did cause some limited damage to Galatea's reputation as a hero.