If the the loose strand of carpet is short I would just cut it off with some duckbill knapping shears. You can pick up a pair at Home Depot for under $20. If the loose carpet fibers are long like on a berber carpet I would glue it back down in the carpet run with a hot glue gun with a long tube tip so you get the glue only on the backing of the carpet and not on the top of the carpet fibers and push down on each bend of the carpet strand. Cutting the carpet fibers will make it so it won’t get worse and get snagged by your vacuum cleaner. Sometimes gluing the end piece back on the backing with a hot glue gun will help so it does not come loose. I also think it looks better without the long loose strands of carpet, this is why I always carry a pair of napping scissors in my side pouch when I am cleaning the carpets in your home. I also have a carpet glue gun if I need to glue the carpet fibers back down on the backing of the carpet.
In this video you can see when I was carpet cleaning and I noticed a lot carpet fibers where the seam is on the carpet, so I trimmed the loose fibers to make it look better and so the loose fibers will not get snagged by the vacuum cleaner.