The words fabric and cloth are used in textile assembly trades (such as tailoring and dressmaking) as synonyms for textile.
However, there are subtle differences in these terms in specialized usage.
Textile refers to any material made of interlacing fibres.
Fabric refers to any material made through weaving, knitting, spreading, crocheting, or bonding that may be used in production of further goods (garments, etc.). (source)
So can hamsters eat fabric at all?
Yes they can eat through it if necessary.
Its not good for them though, as it doesn’t even provide a good material for them to chew.
With that in mind, it is a material to avoid putting in their cage.