I'd argue that an invalid string concept would be neither correct nor efficient. Why should all code that deals with strings carry the burden of fallibility of a subset of string functions?
You've mentioned NaN propagation in another comment and I think that's a perfect example of the problem with this approach. Sorting a vector of arbitrary floats is a notoriously thorny problem because any float could be NaN, and as NaN is incomparable to any other float, there is no total ordering of floats. There is no general solution to this problem that doesn't involve making assumptions that could be faulty for some applications.
Please support your argument against correctness by providing an example where an INVALID string as input to a suitable modified generic string function would result in a valid string.
I would expect an invalid string to have an invalid length. For integer-valued lengths you'd have to use a negative number to differentiate from a valid, empty string. But then the sum of the invalid-string lengths differs from the length of the concatenated invalid strings. Which is wonky.
Safe string manipulation never exceeds the bounds of the buffer. So negative values are dangerous, as all as any additions that would exceed the maximum size.
Negative lengths are not compatible with unsigned representation.
A system implementing invalid string values must choose a text encoding such as UTF-8 that supports the concept of an invalid character. Null termination is too flexible. As such is simple length prepending.
I don't understand the fallibility.
Clearly misuse of string functions is epidemic.
A propagating INVALID string result makes it very clear there is a logic error and not an exploit.
I understand how one could shoot down implementations, but none has made a convincing argument about shooting down the idea.
You've mentioned NaN propagation in another comment and I think that's a perfect example of the problem with this approach. Sorting a vector of arbitrary floats is a notoriously thorny problem because any float could be NaN, and as NaN is incomparable to any other float, there is no total ordering of floats. There is no general solution to this problem that doesn't involve making assumptions that could be faulty for some applications.