Is it safe to use frayed MagSafe with outer insulation part is broken I have a frayed 60w MagSafe with outer insulation / coaxial part is broken where some wires are cut (some are not). There's no problem with inner insulation part and the MagSafe working just fine when plugged to my MBP (I seal up the broken part with electrical tape). 

My question is, is it safe to use MagSafe with broken outer insulation (some wires are cutted out)? 
Will it damage my MBP especially the logicboard in long term? What the purpose of the outer insulation part?

Update : I have already sealed the cable when I created the post, so I will use image I found on the net to illustrate the situation.



This is my magsafe look like after sealed by electrical tape
Will it damage the logic board?

No.  The shielding is also the ground conductor.  So, you need it for two reasons.  If you cut it, you’ll be breaking the MacBook’s connection to ground which of course will affect it’s ability to function.  It’s like disconnecting the negative battery terminal from your car or any other battery power source - it will fail to function.

Will the &quot;cracked&quot; wire of a MacBook charger eletrocute me

It’s not “dangerous” to you, but if you were to somehow send voltage down this line you could damage your charger and/or Mac.  However, those vintage Mac laptops had a separate (replaceable) DC-in board that would take the brunt of any surge.  If there was damage, it would be contained there.