Phantom voltage, probably
You're saying all your loads died completely (not dimmed, died) and that your inexpensive digital DVM is reading 80 volts open-circuit on the disconnected wires?
That's "phantom voltage" caused by the way inexpensive DVMs work. It should be treated as 0 volts. If you doubt that, go ahead and connect it to a load (you know, like that subpanel right there) and put any load on it - even an old incandescent "night light" will suffice. Does the voltage go away? Phantom voltage. It's caused by capacitive coupling between the wires and has no strength - not even enough strength to move the needle on an analog meter. It is caused when an entirely disconnected wire runs alongside a hot wire for some distance.
So, this suggests a connection problem at the origin (house end) of the feeder, or an intermediate splice. A common mistake is to fail to torque the lugs to the specification called out on the breaker or panel label. Another common mistake is to use a wrong-brand breaker under the misconception that all 1" breakers are compatible. They are not - bus stabs vary enough that the wrong one will arc and burn up the bus stab.
Failures of a wire enroute are exceedingly rare - rarer still if the cable was buried in conduit or direct-buried at proper depth and surrounded by fine material to avoid rock penetration.
3-wire feeders, though
Note that a newer installation requires 4-wire feeder from the main panel - hot, hot, neutral and ground as a wire. Many people get confused and think a ground rod "is the same thing" - no, it is not; it serves a completely different purpose and cannot serve the purpose of a ground wire.
If the installation is old enough that a 3-wire connection is legal, then ground needs to be bonded to neutral in the panel so that at least, neutral can attempt to serve the role of the ground wire. However, this is not particularly safe. While we were banning it, Britain permitted it, and they are now getting taken to school on why it's a bad idea. Note that the failure which causes all the problems is the exact failure you're having right now, except on a neutral instead of a hot. So not "rare" at all.
The other thing is that if any metallic utilities (metal water line; gas line; cable TV etc.) are running between the buildings, the 4th ground wire was mandatory even before 3-wire was outlawed here. That's because you're getting a 4th wire via that other utility, and that means lots and lots of galvanic corrosion on that other utility, or current for which it is not rated.