I'm thinking that it's possible if not highly likely that when Barb dies Chris simply doesn't report her death and thus continues to collect her tugboats (Social Security and the small pension she has from the power company) and thus is able to continue to pay for the 14BLC mortgage and utilities and thus is able to keep the legos and the rest of the hoard.
Old people usually die in hospitals and thus the proper procedures are followed by trained admin staff as to reporting the death to Office of Personnel Management (the federal agency that keeps a list of every living American) and Social Security. Even if a person dies at home first responders are usually summoned by relatives and then the county coroner gets involved and the report is sent.
But since Barb has no family (and I'm not counting Cole since he seems to have cut her loose ages ago) except Chris, and will/has died at home, it's likely Chris just leaves her in the hoard, collects her tugboats, and has a great old time among his Legos and Commodore 64 goddesses and Transformers and the rest of the hoard.
It can take a REALLY long time for Social Security to catch on, I'm talking fucking DECADES, and only when the recipient appears to be 112 years old. Chris could get away with it until he himself is old and gray haired and decrepit. Or Chris could simply die in the hoard, and the only way he's found is via the turkey vultures circling 14BLC.