I was interested in the ide that fibrous plant leaves or stems could be used like that - informal, unprocessed (basically) strings for immediate use in the garden - so did some quick "one click" research.
I found that New Zealand flax can be grown from garden heat zones 11 to 7, with necessary adjustments for plants in the 7 and 8 zones to prevent plant death - the plants just don't like being frozen that completely. I don't blame them, since I don't either!
There are lots of flax options - of the Linum, not the Phormium variety. I mean, there are lots of Phormium (the New Zealand flax), but there are more herbaceous types if only because annual plants breed and develop different species so readily over time. There are lots of the Linum, flax varieties with a wide range of colors of flowers and that grow quickly. They still need 90 to 120 days of growth to finish their life cycle, but you *could* have a small patch of pretty flowers that you keep going just for string.
They grow from garden heat zones 5 to 9, so they do fill in the places where you wouldn't be able to keep New Zealand flax going past that first growing season.
Both New Zealand Phormium sp. and "regular flax" Linum sp. apparently prefer drier conditions and full sun, neutral soil, so I decided to take a quick look at some other options in fibrous plant leaves and quickly gave up on a "quick look" because there are way too many options.
I had thought that some of the longer leaved, more fibrous of the grasses might be good and ... grass plants are out there that have long fibrous leaves. You can make baskets and cord out of a lot of them, but the sheer number of species in grasses is mind boggling.
So, I cheated and hit up the Britannica website - Plant fibers according to The Britannica
They list what seems to be the commercial species name for the plants grown specifically for fiber, with a breakdown of the type of fiber (stem, leaf, seed puff) so you can get the sort of application you're looking for. Fibrous leaves seem to be a heading dominated by Agave sp. which makes sense to anyone who has ever grown or lived around agave and/or yucca plants.
I now have the thought of seeing if I can get a couple of local natives of the Agave family to set up in my garden. They'd make great foundation plantings for under windows, as part of a dryland garden display, or maybe just a fun addition to a "might be an edible" garden.
I wouldn't have thought about the possibility of starting a "might be edible" or "for future string" garden, and I'm looking forward to the planning of it!
Wait. This sounds suspiciously like a new hobby. Maybe I don't want to dive in with plant research and sourcing until I finish a few other things first.