"its" is actually the same for both forms:
A: his her its --> "That's his/her/its ball"
B: his hers its --> "The ball is his/hers/its"
It's just that we don't use the B form very often with "its": "The ball is its" just sounds unnatural (and could lead to the very confusing "It's its"!).
If we are speaking about an "it", it is usually because either we don't know if it is biologically male or female, or it is something that does not have a biological gender.
In both cases, we tend to either use type A construction or use the possessive noun:
"That's its ball" or "The ball is the dog's" or "That's the dog's
ball", but not "The ball is its".
"That's its leg" or "The leg is the table's" or "That's the table's
leg", but not "The leg is its".
Of these choices, "The ball is the dog's" is probably least common, but it is not incorrect.