I think I found a bug, or at least a limitation I haven't seen before now. I had a crane that I used a the heavy duty winch for the cable. Attached to the end was a JS-1 connector and the mini grabber claw from Stockalike Mining Expansion name "Baby Klaw" in the log.

If you leave the scene with a load dangling from the winch cable it's not there when you come back. It's fallen off and destroyed. Looking in the log I find the following message:

[WRN 22:47:51.049] [F: 27918]: Vessel "Baby Klaw" Mini Grabbing Unit crashed through terrain on Kerbin.

This is where the payload at the end of the cable is destroyed. I don't see any messages about the connection breaking, but the winch cable appears to be fully retracted. If this is a limitation of KAS it's managable.

Load hoisted: https://i.imgur.com/uegrT6w.jpg
Go to SpaceCenter and back, Load gone: https://i.imgur.com/Wr5CjsG.jpg

KSP.log
output_log.txt

Alas, it's a limitation of KAS. The old one had the same issue. If vessel hangs on a rope, the game treats it as "flying". If physics stops in this state, the vessel crashes into Kerbin. The connector itself is a part of the winch part, so when it hangs alone, no problem happens. But any part attached to it will be a separate vessel. You may observe the same behavior by simply triggering timewarp. So, the rule of thumb is never leaving anything hanging on the cable.

I turn this issue into feature request. The best approach to have it addressed would be blocking saving or timewarp if anything is hanging on the cable. last time I tried to achieve it, there were no way to block such actions pro-actively (it could only be done post-factum, when it was too late for the doomed vessel). Let's see if in the following versions of KSP there will be a way to block the action.