I've come across it in old tap gland packings. Luckily it was wet and I've heard that the fibres used in rope tend to be longer and less easy to make airbourne. Not had it tested, but once dry it still wouldn't burn or melt and seemed immune to heat damage.
Agree with Artex containing asbestos: sent samples of the textured coatings in my own house to a lab and quite a lot tested positive for asbestos, as did the vinyl floor tiles. Worryingly, Artex is often simply skimmed over, thus hiding it!
Can also be found in pipe lagging, plastic window boards, plastic toilet cisterns, asbestos cement rainwater and roofing goods, bitumen mastics and reinforced bitumen paints.
Basically, almost any house built before 2000 may contain asbestos, and anything pre-1990 probably does, so you have to be eternally vigilant. As a tradesman I always look out for possible asbestos containing materials before quoting, and always warn on quotations that, as I am not qualified to work with asbestos (and to disturb asbestos professionally, you need to be), if I find asbestos, I may need to modify my plan to avoid distubing it, or stop work until the asbestos has been removed by others.
The HSE tells me that the legal requirement is to treat everything as if it were asbestos, unless it is either proven otherwise, or shows strong indications of being something else e.g. wood or metal. I know people who do break the law and I wouldn't want them and their asbestos contaminated tools working in my house!