Rats cope better with hammocks and knitted things. I liked the idea of knitted hammocks but mainly the issue would be with the material used. Hamsters can chew anything and it can cause digestive blockages and serious health problems. So even if it was tightly woven they could chew it and get threads around their teeth or feet. Some hammies have had to have amputations after getting threads round a food or leg.
So generally no material is safe. Some people do have fleece hammocks - no threads - but it can still cause serious health problems if chews so it might need taking out again if a hammy tries to chew it.
I use the rat sputniks as hammocks - not quite the same I know but our hammy loves napping in his rat sputnik, especially if you put a bit of bedding or substrate in the bottom.
You can also get grass hammocks (although I found the one I tried had a few sharp bits), and there are some great tutorials for making hammocks out of toilet rolls and sisal string. Untreated sisal is safe to chew. I thought about weaving a sisal string hammock but didn't because of the feet getting caught issue.
These are the rat sputniks
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They are called something else in the US but same thing. It's a good size for a Syrian.
Erin's Hamsters toilet roll toys video shows how to make a hammock out of toilet rolls
https://www.youtube.com/watch?v=NuPeyD6w-CI
Vectis has a great hammock on this thread - I think it's an egg box type thing - again only use sisal string or rope.
Managing Bar Chewers
People do sometimes use fabric hammocks but anything knitted or crocheted isn't really safe for hammies, and any sign of chewing a fabric hammock it would need to be taken out again.