There's a couple designs for those out there.
Some, the COM or VS can't be below VSS, i.e. they're common-substrate and that would forward bias the diode isolating them. Usually I think these are just special-case or integrated things, or for low voltages where the transient negative voltage can be small.
Others (that usually say they have higher immunity), Vbs can't be below Vdd, or below somewhat above Vss -- something like that. This reflects the signal coupling circuit, which is something like a small high voltage MOSFET pair, driving differential pulses, and that's how the level shifter block actually works. Obviously the body diode of those coupling transistors, and the receiver circuitry, puts a hard limit on that, and it's with respect to supply rails of either side.
Have also seen a few with a limit of like -30V, transiently at least, which I wonder if that involves a series resistor and clamp diode sort of arrangement. Key is that they say output state CANNOT change during such an excursion -- which makes sense, there's no signal voltage for the level shifter to work with at all.
Inverter applications aren't usually switching at completely arbitrary timings anyway, so this isn't much of a problem, but do keep in mind these are stateful circuits -- the high side is triggered by pulses only -- generated from input edges, and remembers what it's doing the rest of the time.
The same caution applies to a number of digital isolators, which are pulse coupled, not continuously modulated. I believe Silicon Labs' ones are such an example? The ADuM family, in contrast, transmits a keep-alive pulse, and if it goes missing, the output times out. So you can arrange for a fail-safe condition, or have a default known state when the input isn't powered up, etc.
I have never, ever seen a gate driver for the reverse case, i.e., common positive supply, large negative voltage range. It's certainly not a common case, but it comes up from time to time, synchronous inverting buck-boost and Cuk for example. (I have done the latter with an inverting gate driver, DC restore circuit, and PMOS; but PMOS suck, so the performance wasn't great.)
Or PMOS drivers of any sort in general, I might've seen a handful? A high side level shifter with "Vbs" below Vs (it wouldn't be a bootstrap anymore) would be handy for these cases, when they occasionally show up. But yeah, very rare. Bootstrapped NMOS are often usable in such a case, but it's a force fit and requires a lot of support circuitry (how do you make a buck converter bootstrap start up in the first place? How do you ensure it stays running once started?)
Tim