You can't infringe a dependent claim without also infringing the independent claim (at least I haven't seen any case where it happened, since dependent claims are subsets of the independent claim). You can infringe an independent claim without infringing a dependant claim. So using your example (and changing "a device as claimed in claim 1" to "the device of claim 1"), if there is a fabric thumb ring made of cotton, claim 1 is infringed, claim 2 is not. If the ring is made of wool, both claims 1 and 2 are infringed.
Let's use a simpler example.
Claim 1: A method comprising step A.
Claim 2: The method of claim 1, where step B follows step A.
Claim 3: The method of claim 2, where step C follows step B.
If I perform a method that consists of step A followed by step D, only claim 1 is infringed. If I perform a method that consists of step A followed by step B, claims 2 and 3 are infringed. If I perform a method that consists of step A followed by step C (but no step B), claim 3 is not infringed, claim 2 is not infringed, but claim 1 is infringed.
Given all this, one might ask why dependent claims exist at all. After all, if you can't infringe the dependent claim without also infringing the independent claim, where is the benefit of a dependent claim? One answer is that the limitations in the dependent claim may allow that claim to survive if for some reason the independent claim is invalidated. So returning to the example, imagine that somebody else published a description of the method of step A prior to the priority date of the patent. However, imagine that it was novel and not obvious to follow step A with step B. In that case, the dependent claim should be valid over the prior art even though the independent claim should be invalidated.
Probably too much of an answer for the question that was asked, so let's boil it down: Yes, it is infringement (of the independent claim) when a product matches the independent claim but differs from the dependent claim.
Hope this helps.
