I have encountered this totally useless object at several hotels and motels recently, so there must be a name (phrase or word) for it in the hotel/motel industry.
If it covered the entire surface of the bed, it would be a bedspread, but I estimate it covers only the bottom 20% to 25% of the bed. The term that popped into my mind was bedspread bikini, but a bikini, however sparing of material, covers both the bottom and the top with a large gap in the middle. Bedspread monokini? It resembles a scarf more than a bathing suit, so maybe Bed foot-scarf? But foot scarf doesn't make any sense.
Rather than fanciful words or phrases, I'd really like to know what the hotel industry calls this truncated beadspread-oid thingie.
What is the purpose of this __________ covering the foot of the bed?
@StoneyB says it is a bed runner. The picture in his link is not exactly what I saw recently. What I saw covered the entire foot of the bed and fell to the floor on each side -- I don't remember if it fell to the floor at the foot. And in one case, it was on top of a bedspread. He has probably given the correct answer, and bed runners are just getting larger.