Electronic – Powering a breadboard with USB

It's difficult to generalize this sort of behaviour. Some power supplies will work at less than the minimum load but with degraded performance. Other power supplies may shut down, and others still may malfunction badly (oscillate / shut down). Others may behave perfectly.

Quite often, basic power supplies use pulse-width-modulated (PWM) toplogies with inductive storage elements. The switching frequency is fixed and duty cycle is varied to control the output voltage as a function of load and input.

When the current in the inductive storage element never goes to zero, the converter operates in two states - switch on and switch off. This is called continuous conduction mode (CCM). Once CCM is achieved, the duty cycle essentially doesn't vary (unless the input changes) - the converter behaviour doesn't change with load and things are fairly consistent.

At very light load, there isn't a DC current level in the inductive storage element. The converter now has three states of operation - switch on, switch off and inductor current decreasing, switch off and inductor current = 0. This is called discontinuous conduction mode (DCM). In DCM, output load affects the duty cycle as well as input variations.

Most controllers have a minimum PWM on-time that can be achieved - if the plant tries to command a duty cycle lower than this minimum, you may see erratic output, missing pulses, high ripple current, etc. - some converters will simply stop regulating (the output will rise). Some controllers detect this and go into controlled burst mode to keep the output loosely regulated.

Also, the feedback loop compensation will be dictated by the CCM performance of the converter, since there are nasty things (like right-half-plane zero) in CCM that need to be stabilized that essentially aren't there in DCM - the compensation may be sub-optimal and things like transient response will be affected.

If you don't connect the grounds of the two supplies together, you don't have a circuit.

Assume for a moment that you don't connect the two grounds together. You connect the microcontroller's data out pin to the LED strip's data in pin. The LED strip determines if your microcontroller is sending a 1 or a 0 by measuring the voltage on the data pin compared to its own ground voltage - but since its ground isn't the same as the microcontroller's ground, it could get nearly any result. At best, the two devices won't be able to communicate, and at worst the voltages will be so wildly different that one device or the other will see a very high or very low voltage on the data pin.

Connecting the two grounds together means you have a circuit; everything is working from the same ground reference, and power can flow from either supply, through a device or devices, and back into the supply via the shared ground.

You're right that connecting grounds together can in certain cases cause a problem; this happens when both devices are already referenced to different ground voltages. For instance, one might be connected to a local power supply, while the other is connected over a long cable to a power supply a long way away on a different AC circuit; there's nothing preventing the two having different ground potentials, creating what's called a ground loop. There are various ways of isolating two systems but still transmitting data between them in situations where this can happen.

In practice, however, either one of your grounds will be floating - that is, having no external reference - because it's running off batteries or otherwise has no other ground connection, or both your grounds will ultimately be referenced to the same voltage; for instance, when you have two devices both plugged into AC power from the same distribution board. In such situations, connecting the grounds together is both safe and necessary to complete a circuit.