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That looks a lot like someone ripped out parts of the front panel LED cluster, and fed it out through a ventilation hole.
Good news is chances are it is unlikely to kill your dog or cat, or to set your house on fire. Its also unlikely to damage your system, depending on what the other cable is. If its your power switch, and it breaks, turning your system off and on again would be interesting. At most this is 5V at very low current.
On the other hand, no professional and a good chunk of petty dabblers would never leave a wire out like this except when bench testing. This is a clear sign you need to find a new 'system repair guy.' This shows an extreme inattention to very large details, and he might miss an actual issue in future.
Send this picture to his boss, and demand that its done right by someone who knows what he's doing. I'd be more worried about what kind of butchery is done elsewhere inside the system.
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He shouldn't have left it like that without at least explaining. In his defense, many cheaper PC cases are made out of crappy plastic, and break easily. He probably removed the front panel, or it fell off, and the plastic parts that are supposed to hold the front panel LEDs in place broke. Rather than hiding them inside the case, he pulled them through the front panel, so at least you can still see the LEDs.
If he broke it, he owes you a case. – Tetsujin – 2015-09-14T08:36:07.860
2“Why?” is a fairly big question. Maybe the repair guy was lazy, drunk, incompetent or just non-caring. Who knows. But the big question is why aren’t you asking this question to the system repair guy directly. Was he paid? Is he on staff? Or something else? A badly done job is not finished job. Contact the system repair guy and get him to fix it. And if he can’t, just contact his supervisor/boss and complain. These wires are not dangerous, but I would not pay for this kind of work to be done. – JakeGould – 2015-09-13T05:46:28.213
2I don't think rhetorical questions are on-topic. You know that this kind of work isn't right and people can only guess at what those wires are. They aren't going to cause a problem in the future because you aren't going to leave the system in that condition regardless of whether theiy're dangerous. – fixer1234 – 2015-09-13T06:02:00.480
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Also, there is no way a future visitor with the same "problem" is going to find this question, so I feel it's not helping "to build a library of detailed answers to every question about computer software or hardware".
– Arjan – 2015-09-13T12:20:13.803