Property transactions are on the public record. So, if anyone really wants to know if 14 BC has a mortgage or any liens, just go down to the Greene county courthouse auditors office and ask to search the records.
As for Barb's longevity, even if she was in perfect health (which she's not) she still lives in a trash pile. If her health doesn't fail she could trip and tumble down the stairs and break a hip, or get an respiratory infection from mold or rodent piss.
As for her funeral, I bet Cole would take care of it. They're not on the best terms but I bet he'd still give her a final resting place in a press-board coffin, or cremate and scatter the ashes. Or if she dies peacefully at home, Chris could stuff her body in a freezer and keep collecting her Social Security checks. There are cases of people doing that.