Rigid lace is still a soft lace but has no stretch. There is no lycra/elastane or spandex in the fabric so therefore it has no stretch, but depending on the tightness of the weave and/or pattern, it may still have a little 'give'. This sort of lace is often used in lingerie to add a trim. It may be used on bras and bodices and on the non-stretch parts of other lingerie.