Unlike Resignation, which is mainly about ideas being "abandoned" by your partner, about your dreams, Abdication is a character "vice of deficit" that is more vicious and destructive in other ways than just in ideas - financial, moral, social, even physical neglect of you as a partner, may be a portion of Abdication. A vice stemming from what would otherwise be a character virtue of Authority. It is taking too little authority over achieving a goal, like shunning all responsibility for your welfare, your function, upkeep and every other "basic" decency one would expect in any partnership, let alone a romantic one. Like any feature of psychology, Abdication can have a range - from mere "neglectful" behavior, all the way to outright passive-aggressive sabotage of your dreams and your welfare as an equal partner. In Abdication, the partner is likely trying to indirectly control or change the other partner in some way, to fit their own life's goals - their "mission in life" or "purpose in life."
However, they may also be doing it unconsciously, simply to dispense with their own anger or rage, and finding the least-effort, most passive way to steer the relationship only toward their own life's goals. You may notice right in that statement that the Immature Ego Defense, called, "Passive-aggressiveness" would be used in order to express Abdication. (Learning about the Ego Defenses, you will find them to be a handy, objective measure of a personal character maturity level.)
It is pathologically narcissistic to be abdicating of course, given that it produces destructiveness, a "win/lose" behavior - causing what you might call, "relationship rot," or using the phrase, "rotting from the inside out," passive with hostility for no good purpose, manipulative, or just outright neglect, Abdication may come out early in codependence, when one or the other partner either consciously or unconsciously seeks to dominate all the psychological resources of the couple, eventually.
The other vice of Authority as a virtue is called, "Tyranny," where a person "takes over control" of many aspects of the other partner's life functions in terms of Authority.
Someone who uses "abdication," is by definition, controlling in nature, of poor boundaries, narcissistic, and disregarding of the sacrosanct nature of your "purpose" or "mission" in life. Your life's goals and dreams are the most precious things you have, more even than the romance itself. Abdication, or neglect, directed counter to the goals and dreams of a mate shows poor boundaries and a lack of respect for the very life of the other person, beyond even their ideas or emotions. It is their spirit itself - their masculinity or femininity - that is at risk of being hijacked or depleted, and needs their own recapturing of equal Authority in the relationship as its virtuous cure.
As a vice which makes partnership within relationships fail to get to goals, and intellectually unattractive, consider Abdication to be negative in many ways, including in sexual attraction, since it actually depletes the reserves of one's own, or the other partner's masculinity or femininity, making them less attractive and feeling less attracted back to you.