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
A subtle shadowed checkered pattern. Increase the lightness for even more subtle sexiness.
Source Josh Green
Sharp pixel pattern looking like some sort of fabric.
Source Dmitry
Derived from an image that was uploaded to Pixabay by darkmoon1968
Source Firkin
Imagine you zoomed in 1000X on some fabric. But then it turned out to be a skeleton!
Source Angelica
From a drawing in 'Artists and Arabs', Henry Blackburn, 1868
Source Firkin
A background formed from an image of an old tile on the New York Metropolitan Museum of Art website. To get the base tile, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
From a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin
A playful triangle pattern with different shades of gray.
Source Dimitrie Hoekstra
You don’t see many mid-tone patterns here, but this one is nice.
Source Joel Klein
From a drawing in 'The Quiver of Love', Walter Crane, 1876
Source Firkin
A dark one with geometric shapes and dotted lines.
Source Mohawk Studios
A dark background pattern/texture of a dimpled metal plate.
Source V. Hartikainen
Remixed from an image that was uploaded to Pixabay by CatherineClennan
Source Firkin
Derived from a PNG that was uploaded to Pixabay by nutkitten
Source Firkin
Prismatic Hypnotic Pattern 2 No Background
Source GDJ
More carbon fiber for your collections. This time in white or semi-dark gray.
Source Badhon Ebrahim
A seamless background drawn in Paint.net and vectorised with Vector Magic. The starting point was a photograph of drinking straws from Pixabay.
Source Firkin
Remixed from a drawing in 'A Girl in Ten Thousand', Elizabeth Meade, 1896.
Source Firkin
Prismatic Polyskelion Pattern No Background
Source GDJ