Frame challenge: there are silks that may survive, but silk just isn't the material you want.
If you use silk
Modern silks are flimsy because the raw material is expensive and modern people value price over quality. A cheap silk sells better than an expensive one, even if it's low quality.
A sturdy silk needs to be:
- Heavy! There needs to be a lot of material to make it sturdy and it needs to be much thicker than modern silk scarves. Take a look at heavy silk kimonos or early Victorian dresses in museums for inspiration (it was fashion to show off your wealth with lots of heavy fabrics).
- Tightly woven. Since silk is a luxury good, it's often woven as satin (very shiny but has long exposed threads that snag easily) or brocade (multi-colored weave, often with metallic threads). You'd probably want a herringbone or plain canvas weave for best durability.
- Wearing heavy silk makes you sweaty. Silk fibres don't transport moisture very well and the thicker the fabric is, the less air it lets flow through for cooling. Other fibres like linen are much better at keeping the wearer dry and cool during strenuous activity.
- Silk doesn't protect you from the weather. It heats up in the sun and doesn't retain much heat in the cold. Other fibres like wool are much better at keeping you cool when it's hot outside and keeping you warm when it's cold outside.
- Silk is hard to produce. Silk worms eat only mulberry leaves, so you need constant fresh supply. Plant fibers like hemp, linen or nettles are much easier to grow or even forage.
The better alternative
For hundreds of years the clothing of medieval European peasants was pretty much exactly what you want: sturdy (because fabric was extremely expensive and the clothing had to keep as long as possible) and suited for daily outdoor wear.
It consists of 2 basic layers:
- A linen undergarment worn directly on the skin. This wicks away sweat and keeps you cool in summer. Additional benefit: linen doesn't cause and retain as much body odor as other fibers like cotton. But it cannot keep you warm in cold weather, you need:
- A woolen overgarment (could be a coat or jacket, trousers or a skirt). It keeps you warm in cold weather, protects you from the sun and light rain, and protects your body from dirt. Wool undergoes a natural process of felting over time, which interlocks the fibers and makes it sturdier than other fibers. Since wool doesn't transport sweat and moisture, wearing it directly on your skin is very uncomfortable and you need the linen undergarment.
As with the silk, the weave determines much of the properties of the fabric. A plain canvas weave is the easiest to produce, but a herringbone weave can make the fabric sturdier and stiffer.
Laundry has changed a lot over time, but there is consensus that the outer wear wasn't washed often, sometimes not at all. At some time in history it was common to wash your underwear every day (at least in higher social classes), but not your body. Since everyone was equally unwashed they all had more or less equal body odor.
I don't know of any fabric that can resist salt water for long. As soon as the water dries, it leaves tiny salt crystals behind. Those either cut the fibers or make them brittle and rip. A thick salt crust can simply break the fabric like a flimsy cardboard. Any "primitive" people living by the sea are clever enough to either take their clothes off or rinse them in fresh water afterwards.