Jezebel has a very rude character, making no secret of her doubts in the Sole Survivor's abilities and wastes no opportunity to belittle their allegedly minuscule intelligence. She is fully aware of her hostile personality and even mentions it to the Sole Survivor at one point. Saving and rebuilding her doesn't change her attitude in the slightest - she will vocally complain about her new body even if it is composed of nothing but the highest-tier components.
Compounding Jezebel's unfriendly behavior is the fact that she is a prime example of many robobrains' tendency to misinterpret orders and follow their abstract logical reasoning to highly dubious conclusions. During the conversation following her rebuilding she mentions that she is, in her opinion, helping the human population of the Commonwealth. When pressed by the Sole Survivor how she can possibly claim to be helping humans when she is actually killing them, Jezebel reasons that the logic of attempting to help humans survive has a 25% percent chance of success, or in other words, a 75% percent chance of the humans dying anyway no matter what she does. She therefore deduced that simply killing them right away is the most efficient solution as it only serves to hasten mankind's inevitable fate and spares them the suffering of their existence.
The Sole Survivor first meets Jezebel during Headhunting as a disembodied robobrain's head deep within the Fort Hagen satellite array where she is held captive by the Rust Devils. She offers the Survivor information on the Mechanist in exchange for her rescue and the Survivor constructing a new body for her. Once her demands have been met, she honors her end of the bargain by revealing the Mechanist's location and how to enter the mysterious figure's hideout. Afterwards, she stays at the settlement where she was reconstructed but may be sent to another settlement. She remains there for the rest of the game, having no other role as a result.
Jezebel continues to wander the settlement she was reconstructed in after Restoring Order has been finished, behaving like a normal automatron settler, including the option of modifying her robotic body. She cannot be recruited as a follower and offers no interaction apart from rude comments when spoken to.
If killed, her body will remain at the place of her "death" indefinitely and cannot be moved due to its weight. If she was built using only the stock automatron model, she will be light enough to be moved.
Other settlers will treat Jezebel as a settler and will turn hostile if she is killed.
She can be assigned like other settlers to tasks in a settlement, although assigning her as a trader isn't recommended as she will refuse to trade. She can also be assigned to a guard post and can be used to set up supply routes. With the Vault-Tec Workshop add-on, she can be assigned to operate a barber chair or surgery chair with no interference.
If Liberty Prime has been rebuilt for the Brotherhood of Steel, when Jezebel remarks on the body made for her, the Sole Survivor can sarcastically comment on how they were going to use Liberty Prime's body for Jezebel, but ultimately settled for the body that was made for her. If Liberty Prime hasn't been rebuilt or hasn't been discovered yet, the Sole Survivor will make a more generic joke instead.
After receiving a new mechanical body from the Sole Survivor, if Codsworth is beside the Survivor, Jezebel will say that she is such a great robot compared to "that" Mister Handy. As the result, if the Survivor kills her immediately after the dialogue, Codsworth will love that.
If you place her on the body of an already existing automatron before equipping her head, remove all items from the automatron, Jezebel can not be traded with therefore you may only pickpocket your items back if she has been given legs.
Jezebel's head will be removed if she is given a Nukatron torso (included in the Nuka-World add-on), allowing her head to be replaced with that of another robot type.
Early in the conversation Jezebel mentions that Rust Devils believe whatever she says and that it's been to her help. Later when asked how she can be trusted, she says she is unable to lie.
The following is based on unverified behind the scenes information and has not been confirmed by canon sources.
Jezebel can be found in the same room as Ahab. This is probably a historical reference to Ahab, the seventh king of Israel, and Jezebel, his wife.
Jezebel is the root of the name Isabel, making her and her creator share a name.
Jezebel's story is very similar to one in the Silver Shroud radio show, where the severed head of a robot leads the Shroud to defeat the Mechanist. This is supported by some of Isabel's alterations to some Silver Shroud artwork and her having an Unstoppables comic book.
End of information based on unverified behind the scenes information.