Do the rest of the lights in a string stay lit if one bulb goes out or is missing?

ALL the bulbs will go out if you have one strand of 50, and you'll have to go through the trial and error of finding the one burnt out. If you have five strands of 50 and one bulb goes out, then, still ALL 50 bulbs on that one strand will go out but the other 200 lights in the other four strands will stay lit. It is a hassle. If it wasn't difficult to remove one strand and replace another (wrapped on a tree, or hung where you need a ladder to get to it), it would be easier to replace a whole strand when a bulb went out than find which of the 50 is the problem.

The LEDs are in circuits of 50. 1 out will affect that circuit only.