It's typical for production companies to be insured against loss... this often requires types of insurance for some of the key performers (these kinds of secondary insurance often involve health exams and/or binders/bonds). I would imagine with all her problems, every single production Lindsay Lohan is involved in takes out some kind of seriously high falutin insurance policy on her so that in the event she does something stooopid (again) which gets her incarcerated (again) and production is scrapped (again) they're not financially screwed. In hiring someone with severe health problems, like Larry Hagman, I would think Warner Bros., TNT, etc all had policies on him which required a physical exam or medical attestation. Even if he wasn't all that forthcoming with everyone about his medical situation, I can't possibly believe the production company behind Dallas didn't know what they were dealing with. It's always a potential any lead can pass away unexpectedly at any time but given his health and age, it was perhaps more of a possibility with Larry Hagman.
As an aside, the original matriarch was Miss Ellie and patriarch was Jock.