The other womenfolk in her family are flighty twitterers. They are always losing things and leaving things about and forgetting things. They lose men. They lose jobs. They lose apartments.
Rings are pawned. Cars are repossessed. Magic augmentations are disconnected. There is a constant complaint about being let down, or being treated badly, but they are mostly cheerful about their lives, arguing back and forth about who has cleverly gotten the best latest flashy object, contract, or relationship.
Sums has learned not to enter their contests. They think of her as dull and stodgy. They see dull and stodgy as being the next thing to being mentally retarded. I think Sums has to be the third-born of the flock.
If her mother and sisters knew that Sums had savings, they would be constantly nagging for money, so she allows them to think that "freelance bookkeeping" doesn't pay very well. They still ask for loans, of course, but in a pro forma sort of way, with no real expectation of success. A small trickle of small bills that are never returned keeps them satisfied that she isn't hoarding things away from them.
If the requests come too close together Sums would be happy to lend x a bit as soon as y pays back the z that she borrowed last week.
I think I just thought of a way that this information could be entered into the story in an active way (Muppet flashback: "it's plot exposition, it has to go somewhere!"). The spider Mage, after incapacitating Sums and Chaz, ransacks their pockets and equipment. He plays voice mail left by her sisters and mother, embarrassing Sums. I think I'll call this point b.
Point a is the initial meeting with spider Mage and his surprising but inevitable betrayal (Firefly flashback). Point c is the argument with SM and his decision to experiment on Chaz while leaving Sums free in the warehouse to do the audit of magickal energies that she was hired to do. I think the tipping point is that she's only contracted to work for the city, she's not an actual government worker.
Chaz is much younger than he looks and much better looking. Sums knew that he was using sartorial magic to make himself look more middle aged, and that he felt that gave him a look of authority. Actually, he comes from a family of well known politicians (I think, maybe) and he's working as a mid level municipal bureaucrat because that's the only way to use his training without entering the fray that he can think of.
Spider mage's family has actually used him up, drawing magic through him from the time that he was a child. This is where I need to know more about how magic and this society works. There's something brewing in the back of my brain. I think it includes the type of magic you can do being influenced by your outlook or worldview from childhood through puberty. I think this must mean that children's books are heavily regulated.
I keep trying to consider how a society with no public education would work. I think this is a good excuse to read Dodger, which Pratchett just released. The Victorian way was with nannies, governesses, tutors, and boarding schools. And apprenticeships. I suppose indentured servitude would fit in there, too.
I think for my reader's sake (Asimov flashback: Gentle Readers) spider needs to be actually dying at the beginning of the story and have the chance of being healed at the end. (The recurring flashbacks are giving me a Vonnegut flashback: So it goes.)
I think that the stated tipping point for spider deciding to let them go is that Sums has determined that some effect from the spam filter is slowing his decline. The unstated, and possibly unconscious, tipping point is the realization that all three of them are estranged from their families. Sums has pulled back from hers while allowing them to continue in her proximity in complete ignorance of every important thing about her.
Chaz has a less successful estrangement, in that if his family learned of his location and position, they would lean on him. He is successfully free of them only because he realizes that he would not be able to withstand their manipulations and therefor does not risk any contact at all.
Spider also has completely cut himself off from his family. They do not realize this. They are expecting him to be dying and are willing to allow him to take himself off to indulge in his hobbies as his power wanes. They still know his location, however, and still consider him to be a family resource. If they knew that he wasn't yet as sick as they thought, they'd collect him.
Because they are magic users, staying off their radar is much more difficult and more fraught than Chaz's escape is. Chaz is going to babble when the spiders wrap his head (their webs interfere with information transfer). I think one of the things he's going to babble about is kidnapping and ransom. Possibly he arranged his own.