I've been going through this same situation in my family. I have a mentally ill brother, and I'm the only sibling. Luckily my parents are organized and are involving me in the preparations, and I am planning to take over his care once they die (not happily, but I am doing it). Please excuse the length, but hopefully this will be helpful to you and others.
Even if you do not want to care for Jenny, I strongly encourage you to get involved now with your parents and make that wish known (do they know this???), and help them make plans for their own care and Jenny's.
There are a few issues here which you have to separate a little bit, though they of course overlap:
1) YOUR PARENTS' CARE -- this involves their will and how any remaining assets will be distributed, their revocable living trust (RLT) for their assets if they have one, their POA, their healthcare POA, long term care insurance, life insurance policies, etc. What you want to counsel them NOT to do is make sure that no assets go directly to Jenny. Also, they should perhaps not choose Jenny as POA since she's not able to handle it. So decisions need to be made on who will do what and those folks need to be aware of what their roles will be. You should also know their general preferences -- do they want to remain in their home, retirement center, etc.? What can they afford? Of course, everyone needs to also understand that preferences and plans may have to go out the window when you actually get to that stage, kinda like labor when you have a baby!
For your parents, I agree with the PPs -- if you plan to be primary caregiver for them, or at least involved, you need to know their will is done (you don't have to see it I don't think), and you need to ensure their POAs are set up (even if you are not the person they select). The important thing is that these docs are in order and everyone knows who's doing what when the time comes, including who will be primary to care for Jenny once they die. As your parents decline, that person(s) needs to be "trained" by your parents and start taking on the caring role because your parents will be too ill to do it, and because Jenny will need to get used to someone else playing this role. That will make it less of a shock once they die -- hopefully by then, she will be used to whomever has taken over, and it will give her peace of mind that her needs are being planned for.
Along with that, I totally agree it would be good to have some frank conversations about their assets/income to address the issue of whether they have "enough" money to care for Jenny in the way they want to before they die. Or will someone else have to help financially? Where you could run into a problem is if they are still alive, they run out of money, and you're faced with requests to support them, much less, to support Jenny, since they can no longer afford to.
2) JENNY'S NEEDS -- the Special Needs Trust (SNT) which is SEPARATE from the parents' will, her housing needs, her income (SSI, etc.), healthcare, transportation, etc.
HEALTH: I'd strongly suggest that while your parents are alive and presumably have more free time than you do, to work on setting up more foundational supports for Jenny. For example, healthcare. She may already have Medicaid since she has SSI, but verify that. If not, your parents should get something in place now (whatever she qualifies for) even if she doesn't use it right away. They should also look into the local mental health system (probably a county outpatient clinic) and find out how it works, and if she needs to get into their system so she's set up in case she has a crisis later on. Does she need to go and do an initial intake with them? Will she even go? Does she need meds regularly?
MONEY -- Your parents are probably managing her money right now. If not, SS has a thing called "representative payee" which means SS designates someone (usually a family member) to manage her money for her if she's not capable of managing money. My brother has it; it's a godsend. Dad receives the SSDI money and makes sure bills are paid, allocates some for groceries, puts some in his savings account, and my brother gets a monthly allowance to spend on whatever he wants. Definitely get this set up with SS before your parents die. It would probably be best if the SNT trustee acted as Representative Payee -- that way they have control over all finances and can determine what to pay out of the SSI and what to cover from the SNT.
HOUSING: It would also be good for you to know how much her SSI gives her monthly and how far would that go once she is on her own? Will she be able to live your parents' home? Do your parents need to sell the home before they die to use the money toward a nursing home, or do they have other assets? Does she have the capacity to care for the home? (If not, a family member could help with that, or you could hire someone to act as a property manager.) While you may say "no way can she live there!" I caution you to think twice. Housing for the mentally ill is terribly difficult to come by -- long waiting lists, and then they get kicked out because of bad behaviors (like drug use!) and have to start all over, or they have bad credit and can't get approved to rent, or they can't manage money and pay rent on time, etc. It may be a very prudent thing for you to consider either keeping the house for her to live in for the rest of her life, or selling it and using the money to buy something for her. And it would probably make everything a ton easier having the housing taken care of and not be in jeopardy if she slips up, worry if she were to be homeless, etc. I have so much peace of mind because my parents bought a place for my brother to live in that's paid for, and our SNT will help cover insurance, taxes and maintenance.
PAPERWORK: My parents have shown me the SNT but not the will. However, Dad says that the "plan" is that their RLT holds all their assets, and the will says "upon our death, take $x from the RLT, and transfer it into the SNT." The SNT is a separate trust doc. I do think it might be helpful for you to read the SNT to get the flavor of it, what kinds of expenses the SNT is designed to cover, etc. We have a clause in ours that says that my brother is never to know about the existence of the SNT (so we don't get calls begging for money). Usually SNTs are written broadly with guidance that the trustee should first allow any benefits (SSI, Medicaid) to pay for expenses and then trust is there almost like a "secondary payer" to cover any additional expenses, and it can also be there to help in case she ever loses SSI.
ROLES: Here's a biggie: SNT Trustees are there just to pay bills and to make sure the trust is properly invested. And the SNT Trustee can be a family member, or you can hire a lawyer or CPA to do it, and they get a percentage of the SNT for their time. They DON'T arrange housing, figure out healthcare, answer calls in the middle of the night, or act as a social worker. Jenny needs someone -- a family member, a social worker from the county, someone to be her "care manager." They essentially fill the role your parents are now for the areas where she cannot manage her own life. And this is why your parents should talk to their local mental health dept at the county now -- can they get these "care manager" services from them? Or what other resources are available locally for that? Sometimes non-profits do it too.
The care manager person looks at the big picture and makes sure everything is covered. Then the care manager would hypothetically work with the trustee to say "Jenny needs x, can you pay for it from the SNT?" And the trustee says yes (or no) and then pays the bill or makes the purchase. In my experience, finding someone to play the care manager role, if you don't have a family member to do it, is the HARDEST part of about helping a mentally ill person. This is a real missing link in our mental health system and usually it is family members that play this role because the local government doesn't have the resources to do it. I have learned that some non-profits will do it, but they can charge $80/hr to do it -- for things like taking the person to the doctor, grocery, and more complex things like arranging housing and working the system locally.
Any family member who is responsible and willing to play a more hands-off, behind the scenes role could act as the Rep Payee and Trustee -- you could do this from afar as long as you had a care manager. It is the care manager role who needs to be hands on with Jenny and work directly with her to manage her life.
I am sure there is more I could say, but it's late and I am sure I have already freaked you out! Do some reading, do a lot of talking with your parents, and if they are willing, encourage them to attend a NAMI Family to Family Class (
http://www.nami.org/Template.cfm?Section=Family-to-Family&Template=/TaggedPage/TaggedPageDisplay.cfm&TPLID=4&ContentID=32973). That will help them think about preparations and network with other local parents who have been down this road.
Also - a great blog on these issues by a woman who is caring for her mentally ill sister:
https://trophydaughter.wordpress.com/
Good luck!