Hoping I am understanding what you are talking about I am pretty sure you are reffering to the lasso, commonly seen in roping, cowboy movies, and so on, though not used in everyday things like show jumping and dressage.
The two commonest names are Lariat or Lasso
A lariat is a long light rope in the form of a lasso or noose which is used to catch running cattle.
A rope or noose it scares me that you want to know this though
lasso
A noose is a piece of rope usually used to hang somebody.
A rope that hangs a person is called a noose.
Throwing a rope loop (a cord with a running noose at one end) round an object by twirling it over your hear first.
Noun1.reata - a long noosed rope used to catch animalslariat, riata, lassorunning noose, slip noose, noose - a loop formed in a cord or rope by means of a slipknot; it binds tighter as the cord or rope is pulledrope - a strong line
noose
Noose.
a noose
noose