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I started with printing on fabric stretched across the building plate, but soon I have realized, that better result can be achieved with fabric frozen inside the print. With 'pause at height' plugin in Cura ask the machine to stop the printing when half of the part will be completed (1 mm for a part of total height of 2 mm) and to lower the buildplate for 50 mm or so. When printer will pause the printing stretch a piece of mesh-like fabric (I played with my wife's stockings, but best results achieved with mosquito screen) and fix it with scotch tape. Unpause the printer.
You could make a lot with that technique, just make sure that the fabric thickness is less than the layer height.