Yes, a frozen starlight can break!
The starlight is used to awaken the boss Yakchal. You have to go to Formorgar Mines, in Svargrond and find Yakchal chambers (it is near the final mission of the Ice Island quest).
Once in her chambers you have to use the Frozen Starlight in her Sarcophagus. That will trigger her appearance (as well as the appearance of many other creatures, such as Crystal spiders, Ice Golems, Ice witchs and Frost Dragon).
When you use the starlight in the Sarcophagus there is a chance it will break (the boss will still respawn, tho).
EDIT: according to tibiawiki, there is a 10% chance that the Starlight will break in the process.