Hi-my Husband Has Been In A Nursing Home For 13

Hi-my husband has been in a nursing home for 13 years. Just got a call that they gave himm a dppler on both legs. ( he is immobile) Diagnose with deep vein thrombosis. Got an injection & will now start him on Warfarin. My head is spinning! Is this safe? Should I have him sent to the hospital? What happens to all of those broken blood clot particles??