Is there a general rule of thumb for determining what the maximum amount of rear backspacing on a given wheel width can be? I'm trying to determine what the maximum rear backspacing could be for both 10" and 8" wide wheels.

I am not sure that I understand exactly what you are asking. But, the maximum backspace is the same no matter the wheel width. The hub to whatever first interferes with the wheel and tire dictates the maximum backspace. That is why we often use offset spring hangers. To allow more backspacing and thereby get more wheel and tire width because the spring is usually the first thing that limits inside wheel well width.

If you are asking how to determine what your particular maximum back space is, use a piece of cardboard. Jack a rear corner of the car up, slide a piece of cardboard under it, let the car down so that the tire marks the cardboard. Jack it back up and remove that wheel. Now take a plumb bob and trace the inside limits of the wheel well along with the hub onto the cardboard. Very simple and very accurate. Be sure to do both sides because they will vary.

Did that answer your question?

What I would like to know is if there is a limit to how much backspacing a wheel can have from a safety point of view regarding the structure of the wheel. For example, I have a 10" wide wheel with 5" of BS. How much more BS could that same 10" wheel have and still be structurally sound/safe? 6", 7", 8" ? I hope this makes sense.

When my Dart had a stock length rear end under it I ran a 15 X 8 Weld wheel with a 5 1/5" B.S., after installing the narrowed Dana I run a 15 X 10 with a 4 1/5" B.S.. There haven't any issues with either wheel.

Shouldn't be an issue, I have Mustang rims that are 9" wide with 6" of BS.

Wheel manufacturers will not sell a wheel that is compromised with an attempt at building a wheel with too much backspacing. In other words, you will not be able to order one that exceeds the safety threshold.

look at today's front drive wheels. lots of backspace on those without problems.

This is what I was getting at. What is the safety threshold?

It's important to understand the architecture of the steering & suspension design, as well as packaging.
Contemporary designs have moved the hub & spindle outboard, more in line with the way FWD systems are packaged.
Road-course cars have been doing that in front for many years, and have gained cornering speeds & what you could call "predictability".
If one had to put a # on it, it seems that 2"-3" of offset (pos or neg) is about the limit, meaning where the wheel's center is in relation to the edge of the rim.

The most backspacing on any stock wheel I've ever sold was on GM 15x7" wheels: 4-3/8". MOST wheels are right around 4" BS - even on a 6" wide wheel.

I agree with the above and will add that I am sure that it is not 'one size fits all'. Different wheels will very likely have different safe limits. This is a question for the particular wheel manufacturer IMHO.

I hate the look of FWD wheels (full outboard offset) on RWD muscle cars!

The rear wheels on a Gen 1 and Gen 2 Viper are 17 inch diameter and 13 inches wide with a 10 inch backspacing.

As has already been said, wheel manufacturers would build and sell it if wasn't strong enough.
Too much liability if it could meet specs.