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

Yes there are and they are the best, IE, the most accurate speakers made.  Look up Magnepan and give your favorite model a tryout in your room.

Cheers!

Any fully open back speaker could qualify.  There are a lot:  Electrostatics, Maggies, Time Windows... yes they have wood frames, other wise they would droop and sag.  

Maggies! 

Don't forget Vandersteen 4's. All you see is the top & bottom oak caps & that big black sock wrapping 95% of the speaker. 

I've seen pictures of the Vandy 4s sans sock. Very odd looking thing: a very strong central tower of various speaker enclosures (black MDF) attached at top & bottom.

Magnepan, Vanderstein, Dalquist, Thiel, Heil, Ohm all made(make) speakers at least partially covered by fabric (although all but Magnepan,  Quad, and Dalquist had boxes for some of the drivers.)  Going back even further, Stu Hegeman had a partial fabric covered speaker sold under the Eico and the Harmon-Kardon labels.