Might somebody have another blood clot while taking the drug coumadin (warfarin)?

Yes.: There are some patients for whom Coumadin (warfarin) does not adequately anticoagulate (thin the blood), and thus these patients may require alternative medications. Discuss with a hematologist to gain a better understanding as to what options exist. Sometimes this is an indication for placement of a filter device to catch a DVT from becoming a fatal pulmonary embolism (pe).