Satisfied that Chrysalis is permanently bound, Twilight decides to do a little experiment: While Chrysalis will never be released, she could still be reformed. Thus, Twilight takes the former queen as her pet, to train her in good manners and reform her with behavior modification, praise and patience. Chrysalis, understandably, is not pleased with this arrangement, and loudly and vocally voices her displeasure. However, a thick, throat-filling gag takes care of such protests. Since Chrysalis doesn't need to eat or drink anymore, the gag only comes out when Twilight wants her to talk.
The years go by, and Twilight continues trying to teach Chrysalis good manners. It takes a long time, and many training sessions, but Chrysalis finally caves in to Twilight's ridiculous experiment, if only to amuse herself at seeing the princess treating her like a dimwitted cat. But to Chrysalis' surprise, she starts to enjoy Twilight's praise whenever she does what the princess requests. She doesn't say it, but being cuddled and petted are quite… satisfying.
Twenty years after being bound, Chrysalis has accepted being Twilight's pet, cuddle-buddy, and pillow. All thoughts of conquering Equestria or enslaving the ponies have long-since disappeared, and now all she wants to do is be there for Twilight when she comes home after a long day of work at the palace and cuddles the changeling to relieve the stress of being a princess, sometimes in Twilight's favorite latex bodysuit. And though she never thought she'd accept it, Chrysalis has also learned to accept that she will never leave her sack. With a queen's long lifespan, it's conceivable she could still be alive and bound 1000 years from now. But as long as Twilight's still with Chrysalis, that's fine with her.