The break is at the strain relief — the one part designed to flex
The junction where the cable meets the plug has a name: the strain relief. Its whole job is to spread the bending over a couple of centimetres so that no single point takes the full angle. When you see a split jacket there, that part has already failed — every bend is now concentrated into a few millimetres right at the plug, which is why the break grows instead of stabilising.
And inside is not one thick wire. A charging cable is a bundle: the power pair alone is typically dozens of strands around 0.1 mm, and the data pair a few more. Once some of those strands break, the rest have to carry the same current through a smaller cross-section. Higher current density means more I²R heating, more heating means faster insulation ageing, and faster ageing means more strands break. It is a loop that only runs one way, and the heat is what makes it more than an inconvenience.
Why tape makes it worse
Wrapping tape round it feels like a fix because the fault disappears from view — and that is exactly the problem. You have hidden the only warning sign you had, and at the same time you have made the bend worse: the tape is stiff, so the flex now happens at the tape's edge instead of being spread along the relief. The cable fails at the tape edge instead, usually within a couple of weeks, and this time you cannot see it coming. Heat-shrink does the same thing more neatly. Neither changes the fact that some strands are already broken.
Soldering a new joint is the other tempting answer and it has the same fatal flaw: a hand-made joint has no strain relief. You can splice, insulate and tape it beautifully, and the solder blob is now a rigid point in a cable that flexes every time you pick up the phone. It breaks beside the solder within weeks, and a soldered joint that fails can expose live conductors rather than just a frayed jacket. This is one of the few things where the honest answer is: it is a consumable, replace it.
The one test that matters costs nothing
Charge for ten minutes, then touch the plug. Warm — about body temperature — is normal. Noticeably hot means current is being pushed through a reduced cross-section, and the cable is already degrading faster than you can watch it. This test is better than looking, because a cable with a completely intact jacket can be running hot inside: the damage is in the strands, and the jacket is the last thing to show it.
Two other signs mean stop rather than watch. You can see copper, or the strands look black or green at the break — that is arcing and corrosion, and it has moved past "frayed". It only works at a certain angle — that is a partly severed conductor, which is the highest-resistance state and therefore the hottest. Nurse it through one more night if you must, but not on a bed, and not under a pillow.
Choose the next one on five things
Braided or nylon outer rather than smooth rubber — the weave resists abrasion and does not split at the bend. A long strain relief, at least two centimetres of flexible sleeve, rather than a stub of hard plastic. An L-shaped plug if you use the phone while charging, because a right-angle connector cannot be bent by your wrist. Thicker conductors — thin cables drop voltage and get warm even when healthy. And a certified cable, USB-IF or the maker's own programme, because an uncertified one has no chip to negotiate current and no reason to be honest about its gauge.