...Just judging by the pic...The string is still serviceable...that is only one of the fiber bundles that make up a string strand ...there are many in a single strand...if an entire strand is damaged or broken then one is in trouble...
That bundle can be cut, end carefully burnt and weaved back into string...since peep should be tied in that will prevent it from further movement...low poundage wont put strain on string...
Its rare for a peep to jump out even when not serverd in due to moderen strings design with "Z" twist...
Unless the bow was very low poundage it may have been improperly installed...
* Have the peep installed with a press and tie it in...keep an eye on it..
NOTE:** We will get approx a half dozen bows this summer and during hunting season due to broken strings at peep...
A PEEP SHOULD BE INSTALLED USING A PRESS...
-most damage to string occurs with installation of peep NOT using a press...
For peace of mind if unsure... replace strings
Neil