Generally a dance figure rather than a dance but most likely someone, somewhere will have called a dance after it... In the eCeilidh repertoire you'll meet the movement in Bottoms Up or the Witches' Reel. It's a children's game (first recorded in 1744) and it's there in Dicken's description of Sir Roger de Coverley (where it is there in name, although likely not the same figure).
For the figure, you could meet it if you are dancing in set of 4 or 5 couples and you know it's likely to happen if the caller says:
The low risk way of doing it is that the top man ducks and heads between the top and second lady. They remember to raise their arms to make an arch. The top man leads (or drags) the horseshoe of people round through that arch and heads back to place. The second lady has to remember that she's part of this movement and allow herself a quick twist (otherwise she'll get all tied up).
The second half of the move is that the first lady heads at the gap that will appear between the top two men, they will have probably remembered to raise their arms. If the second lady has remembered her quick twist she'll be ok being pulled through the gap with the rest of the horseshoe following her.
Not bad? The call 'thread the needle' is nice and descriptive, you are doing it once one way round and once the other.
The top man ducks and heads between the top and second lady and leads round clockwise. The ladies know all about the arch and decide that standing still is no fun. They head anticlockwise. There will be a point where the leading man (going clockwise at spead) it heading directly towards the first lady and the arch (going anticlockwise at speed) and at this point it is important that the leading man heads under the arch again and leads the rest of the horseshoe through. The leading man gets back to place, the arch gets back to place and the second lady needs twice as much 'twist' to untangle herself. Her clue being to make sure she keeps her arms up above her head and twist underneath them.
The second half flows on, the probably-still-moving top two men make the arch and make sure it goes over the leading and just-untangling-herself second lady - the men going clockwise and the ladies anticlockwise. At the decision point the leading lady head under the arch the second time (it is good in all these cases that the arch remembers and makes it totally clear and obvious that it is there to be danced through).
As above, it's quite likely that there's more enthusiasm than music and you are not quite back to place. Most dances with include a 'thread the needle' will have some sort of catch your breath and "lets get back in time" movement.