A clot, or thrombosis, is what sets off heart attacks, so those prone to heart attacks or other clotting can benefit from small, regular, doses of coumadin (aka warfarin). Rats like to eat their fill of the stuff, until they O.D., which results in internal bleeding. Just because a massive overdose is lethal doesn't mean small doses aren't safe. If rats liked aspirin we'd feed them overdoses of that, I'm sure.
Warfarin is a simple analog of a natural product known as dicoumarol, which was found to be the cause of a bleeding disease in cattle, and is produced by fungi in moldy hay. It has several complications, including a requirement for blood monitoring and interactions with other drugs and even foods. So while it's not a horribly harmful drug, it has its problems.
The ads I see on TV are for a newer drug, which the mfgr claims has advantages over warfarin, and requires no more blood monitoring.
"Warfarin", BTW, is obviously a contrived name. One shouldn't judge books by their covers, nor medicines by their names.
By coincidence, I was teaching my class about the Michael addition recently. Warfarin is obviously made by a Michael addition, so it seems like a candidate for an exam question. 
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