Not a pattern for fabrics, but one produced from a jpg of a stack of fabric items that was posted on Pixabay. The tile that this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
More in the paper realm, this time with fibers.
Source Jorge Fuentes
Prismatic Basic Pattern 2 No Background
Source GDJ
As simple and subtle as it gets. But sometimes that’s just what you want.
Source Designova
Classic vertical lines, in all its subtlety.
Source Cody L
A pattern drawn in Paint.net and vectorized in Inkscape.
Source Firkin
Feel free to download this "Dark Wood" background texture for your web site. The background tiles seamlessly!
Source V. Hartikainen
Pass parameters to the URL or edit the source code variables to configure the graph paper for the division desired.
Source JayNick
From a drawing in 'Hubert Montreuil, or the Huguenot and the Dragoon', Francisca Ouvry, 1873.
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Submitted by DomainsInfo – wtf, right? But hey, a free pattern.
Source DomainsInfo
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Background Wall, Art Abstract, white Well & CC0 texture.
Source Ractapopulous
CC0 and a seamless pattern from a tile drawn in Paint.net .
Source SliverKnight
Here is a new seamless wood texture for using as blog or website backgrounds.
Source V. Hartikainen
Prismatic Isometric Cube Extra Pattern No Background
Source GDJ
Not the Rebel alliance, but a dark textured pattern.
Source Hendrik Lammers
Prismatic Curved Diamond Pattern 3 No Background
Source GDJ
Derived from a drawing in 'At home', J. Sowerby, J. Crane and T. Frederick, 1881.
Source Firkin
Derived from a drawing in 'Historiske Afhandlinger', Adolf Jorgensen, 1898.
Source Firkin
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
If you want png files of thisu can download them here :
Source Viscious-Speed
We have some linen patterns here, but none that are stressed. Until now.
Source Jordan Pittman
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin