Those types of necklaces can't be re-strung, but sometimes you can make them shorter. You'd have to find the part where it is connected together. Most times it is wear there are two beds right close together, with no string between. It will be glued together or there may be a little piece of wire, metal stuck in both bead to hold them together. Pull it out, cut to desired length and stick the metal in the bead at the bottom or glue them together. Hope I explained that right. If you get a chance to take a picture of yours I could maybe help a little better.
Oh, if the beads seems melted together like the ones in the picture you've shown, just cut them out, cut to desired length and try melting two bead together with no string between. Heat with a lighter along one end of both beads and push them together and hold till they harden.
