Yes, if one bulb is loose or missing a string of lights or part of a string will quit working, but the way the strings are wired the outlets still work even if the set goes out, normally. So if you have a plug on each end of the string then power still flows to the next set through the string that is not working.
Most of the twinkle type lights got to where the bulbs are made that if one blows the rest still works, the older types if one blows they all go out, either new or old if one is loose or mising they all goe out. The larger the string the more sets of bulbs in parralel. I think around 35 bulbs in series are one string and if one is loose they all go out. A set of 120 or such is just 3 strings in one set parraleled, so if one bulbs is loose then 1/3rd of the string goes out.
I had some of those 2-3V twinkle lights that gave me fits in a junk string. Sockets always getting loose and then the set goes out and mess with it for a hour or more to find the loose bulb.
Probably all the same thing with the LED types. The set I have is the same as twinkle light sets, just using LEDs instead of a twinkle bulbs seems to be the only difference and perhaps how many wired in series may vary.
I wonder if the AC is rectified to DC and where/how?
I have some fancy twinkle light strings I'd like to change over to LED, lots of settings for fade in fade out, chasing lights, flashing various ways, etc..
Expensive sets, I wonder if I could buy LED strings after Christmas 50% off and just change the bulbs in the sets?
Just buy the cheapest LED strings I can get.