it is VERY MUCH NOT HOW IT WORKS
like, fifteen layers of not how it works
(prefacing this with "I am a lawyer who does this kind of work for a living but this is not legal advice and it doesn't make me anyone here's lawyer, this is me Raging Against The System because I have a lot of feelings about it" and "it is possible that the law is different in Hawaii or that I'm missing some key detail about the plot and thus my criticism is invalid, but I doubt it")
Some definitions before we begin:
Custody: who makes decisions about the kid.
Underlying custody: The default person or entity who has custody.
Guardianship: "This person normally would have custody, but I have a court order here that gives me custody instead for an indeterminate amount of time. However, if something happens to this court order, custody reverts to the person with underlying custody."
Placement: where the kid lives. Not the same thing as custody. A foster parent has placement but not custody.
Permanency: The ending of a case. Achieving permanency relatively quickly is necessary to keep kids out of legal limbo for years and years. That can mean the kid is returned to their bio-parents/relatives, it can mean that they are adopted out of foster care, it can mean that a relative gets guardianship, but it's all permanent (meaning "an indefinite period of time") solutions.
With that out of the way:
Nani didn't enroll her in insurance on time and so can't afford the bill, so she has to let the state pay for it: if they're talking about Medicaid, it doesn't have an open enrollment period with a deadline. You can literally just sign up any time and it applies retroactively to any medical expenses in the prior three months. You don't need to have Lilo in state custody to have her medical bills paid by the state.
Nani is overwhelmed by the responsibility of taking care of Lilo, so that's why she has to give up custody: You don't need to have Lilo in state custody for Nani to get outside help. Literally nothing is stopping her from using the neighbor (or literally any other person! or multiple people!) as a caregiver without the state's involvement. Nani could literally have the neighbor become a guardian through the normal court system, no state intervention needed.
Nani is irresponsible because she didn't sign Lilo up for health insurance, and that's why she doesn't deserve custody of Lilo: Relieving that burden on Nani (helping her fill out paperwork or doing it for her, hiring someone to help organize Nani's life a little better or teach her parenting skills, maybe referring both of them to something like grief counseling or family therapy because grief can interfere with executive functioning skills which makes filling out paperwork and emotional regulation kind of difficult) is the social worker's job. If the social worker knows that there's a problem, doesn't meaningfully help with that problem, and then removes the kid because of that problem that they didn't help with, that's what we in the biz call "lack of reasonable efforts to prevent removal." There's case law in Massachusetts specifically that says that just telling someone to do X and expecting them to handle it themselves is not reasonable efforts. If they could handle it themselves, they wouldn't be in the situation they're in, so the social worker needs to do something more substantial than just bugging people about deadlines or handing them a list of places to call.
It's okay because Lilo is being taken care of by a neighbor, not the state: If the state is paying her bills and deciding where she lives, that means that the state, not the neighbor, has custody. If the state wanted to put Lilo somewhere else with a different family, they could totally do that, because they're the ones making that decision. If the neighbor instead has guardianship, then SHE would be responsible for all of Lilo's medical bills, so we know that's not the case. Now, "kinship placement" - putting a kid with a relative or family friend rather than a stranger - IS a thing in real life, and that CAN translate into guardianship eventually if that's the permanency plan. HOWEVER, see my next point for why it's still a big deal.
Everyone, including Lilo, is okay with Lilo being in state custody, so it's really not that bad: I represent people – parents and kids – who for whatever reason agree that DCF custody is actually the best option, at least for right now. You might have a kid whose bio parents are abusive and so they'd rather stay with grandma, or parents whose kid is physically aggressive in a way that they can't handle and they really want the kid to be in an out-of-home program only DCF can provide. They still get me as a lawyer before that decision happens. Why? Because it involves giving up constitutional rights, and that's not something to be taken lightly. It is not something where they can just sign a piece of paper and hey presto, now you're in foster care: there is still a court process, and there is a court process because it's a big legal decision.
anyway if I was Nani's lawyer I would lose my shit at half of the things that happens to her