I honestly would love to believe this is the case but in my experience the only time I've ever seen this happen was when my daughter was a "shriner's kid". shriner's has an amazing case management program that extends beyond the hospital walls, but between what we experienced with my mom and what I know from working in one state's health and social services department this wouldn't be the norm.
can't speak to other states but at least in California-
low income housing is handled by individual city and county agencies-they do not communicate w/ dshs except to occasionally get a verification of public assistance receipt. no communication w/social security or medical providers.
dshs despite being one agency can't communicate within itself a great deal b/c of HIPAA and other confidentiality laws. unless child or elder endangerment was an issue case management wasn't a service that was provided. granted I retired several years ago, but I just for the heck of it did a quick search to see if California is now offering this-the DID, for a fee-for a couple of years as a pilot program. that pilot was abandoned in 2011 so now there as some very limited services-but only for providers who are discharging Medicaid patients and it utilizes 5 call centers for the entire state (so there's no real personal management going on).
social security disability is handled by the feds-and while they can get info. from social services-it's not a 2 way street. we were precluded by federal law to get any information from them. the disability portion would be handled by the financial side of that house/the Medicaid would be handled by another-and they just handle processing the payments, no patient services to speak of.
the hospitals-well, they have social workers (in the county I worked for-they were our staff members) so they could provide "IGAR" (information, guidance and referral) but they didn't do case management after discharge (once you were no longer in-patient you were really on your own). the hospital my mom used was private so they had their own case managers-and sure they gave you a plan, some information on community resources but again-once you lost your 'in patient' status you were out the door (the follow up care nurse that came to check on mom right after release for the first couple of weeks-that was a contracted private company who just had the instructions they were given upon mom's release-they could advise but they didn't do case management, same with the physical rehab person-made advisements but no management).
it's scary, but there's not allot of medical case management available to most people-disabled or other.