The Apple cables appear to be designed to safely melt without starting a fire in cases where the internal insulation breaks down in case of crushing, slicing, piercing (kittens are even worse than cats in this regard) or simply worn out due to repetitive bending in the same spot.
I've seen people decide to use cords when lightly damaged - sealing the cable with electrical tape. Since the voltage is low on the MagSafe side of the cord, this is more a heat/fire risk than a shock risk. The MagSafe board on the Mac usually protects your hardware from any sort of short - and it also is replaceable if it's fusing blows.
I have on rare occasion seen some nice third party adapters that work with MagSafe connections - but none yet on MagSafe 2. I have seen far, far more dangerous adapters than safe ones.
The worst part of counterfeit adapters is that they typically carry the same "safety" markings as a quality electronics adapter. Also, some have high quality plastics and similar weight so you may have to be very observant to tell a good knockoff from a genuine part. Unless you are using the adapter in an environment where a small fire could reasonably be contained without undue risk to finances or life, you might avoid using a third party adapter if you are not skilled at evaluating electronics for build quality.
The article above explains how the Apple charger is engineered with a processor in the MagSafe connector and a main processor that's equivalent to the original Macintosh - you're getting a computer inside every Apple charger as well as dense and highly safe design shown on the left and a knockoff design on the right.
I've been well served by buying Apple adapters in terms of reliability and safety, despite the higher cost. I know many that have had good luck with quality third party adapters, but wanted to explain the why some third party adapters are dangerous to use and not even close to equivalent to Apple's product.
The MagSafe board is a very easy repair for someone who has patience and a small amount of training fixing any computer at all. The MacBook Pro aren't as fidgety to repair as the iMac and MacBook Air (where I would say you should be a skilled technician with official training materials available to work on them reliably).
You're looking to replace this with a handful of screws turned.
Go to iFixit.com and look up the repair guide and parts list for the DC in board and you will know if you have the skills to find the right part, the right tools and the right manual to undertake this work. Otherwise, pay a local technician to do the job/source the parts/give you what they feel is a good guarantee. As for the adapter, buy a new or used one on the aftermarket or from Apple. When the cord is crushed and frayed, it is designed to fail in a way that won't cause a fire hazard. I wouldn't mess with that end of things or with repairing the transformer itself.
Best Answer
Your solution is probably going to be two things:
If your users are breaking the accessories, you'll want to train them and explain how tightly wrapping or always bending the cord in the same exact spot will break down the materials faster than if they spread the bends across a larger area or just keep the bend radius larger as opposed to a sharp right angle bend.
Note the loop and the straight cable on both the MagSafe end and the power brick end. Also, note that Apple has ditched this design in favor of easily replaceable USB C cords so people that are hard on cables won't need power adapters going forward - just cable replacements.