Refreezing stock after boiling
If the stock has safely been held (under refrigeration for less than 3 days, less than 2 hours cumulative in the "danger zone" [40F - 140F, 4.5C - 60C]), then it would be considered safe before freezing or refreezing. It is always safe to freeze food that was safe to begin with. 

Freezing, and especially refreezing, can sometime negatively affect quality, but I wouldn't expect a noticeable effect on broth. Freeze away, as soon as possible after making it or getting it home. 

Some people freeze broth in ice trays, then store the cubes in the freezer. That way, you only pull out of the freezer what you need that day. Food that was safe when frozen and stays frozen (at 0F, -17C, normal home freezer temperature or lower), will stay safe indefinitely.