Are there speakers with cloth/soft enclosures instead of wood?

Vandersteen Model 1,2, and 3

Yep, and my 2CE Sigs sound fantastic. The cloth covering is also part of the acoustic design and engineering.

Yes, the actual speaker drivers are in a box behind the cloth, but that is rather limited for the mid-range and tweeter, not so much the bass driver and acoustic coupler; Providing for sound coming out around the speaker, unlike a conventional box. Somewhat between an open baffle speaker and a true box speaker.

A box inside the box will set you free

“ none can free us, save our own minds’ “

Bob Marley

please someone report this as a mental agility test for overzealous moderators...

I've never heard Vandersteen speakers, but I will make sure I do before my next speaker purchase. Very intriguing. 

sonus faber made some leather wrapped speakers, IIRC.