The stat likely doesn't wrap around until it reaches 256.

For attack and damage bonuses, the tables in the tabletop game only go up to 25 STR, and if the game doesn't have any data for the STR value, it just uses 0s. (At least it doesn't just take junk data from RAM; then again, junk data would be more interesting, and would result in some specific STR scores that make the character incredibly powerful.)

I don't know how carrying capacity works. If the game uses an exponential formula, I'd expect it to overflow rather quickly, causing strange results. On the other hand, a carrying capacity of 0 would definitely be noticeable; either you'd be obviously encumbered by a single piece of equipment, or the game might use the value as a denominator, and I have no idea of how the game would behave then. (I've seen different games on different platforms handle the division by 0 case differently. In fact, on the Game Boy, SaGa 1/2 handle it one way (yielding a result of 0), while Pokemon handles it another (game locks up, though music continues playing).)

Wondering if the game did, in fact, load junk data. If that is the case, then some Strength scores could result in situations where you get a huge to-hit bonus (only miss on a natural 1 against everything in the game), but a huge damage penalty (only do 1 damage). Or the reverse, need a natural 20 (even against AC 10 or higher), but if you do hit, you just did over 100 points of damage.

Another interesting question is how the game handles low scores, like less than 3. In particular, what happens if you have 0 Strength? What happens if you successfully revive a 0 Constitution character? Underflow to 255 Con?

I could be wrong, but I think it crashed with 0's for stats, but IIRC it handled 1 and 2 strength with additional THAC0 and damage penalties. I don't recall the specifics, I played around with it 30 years ago and my notes aren't that detailed. They just listed offsets and mentioned not to go over $E9 strength or $19 in any other stat.
Again, this was with the Apple IIe version on an Apple IIGS in the early '90s.
I could be remembering wrong as I didn't bother to retrieve my notes, it could have been EF as the maximum.