Carry flag is carry or borrow out of the Most Significant bit (MSb):
CF (bit 0) Carry flag — Set if an arithmetic operation generates a carry or a borrow out of the mostsignificant bit of the result; cleared otherwise. This flag indicates an overflow condition for
unsigned-integer arithmetic. It is also used in multiple-precision arithmetic.
Don’t associate the CF with the sign bit, in a subtraction CF is set whenever the minuend, treated as unsigned, is less than the subtrahend, treated as unsigned.
This is equivalent to an overflow condition, for signed numbers the equivalent flag is OF.
For an (unnecessary?) visual clue, in this 4-5 operation, it is the second borrow, the red one, that set the CF
Not if you subtract from zero, it comes naturally that for any number, but zero itself, you’ll always have the CF set, as the subtrahend has at least one bit set.
Finally, some instructions let you change the sign bit without affecting the CF (see for example the logic operations or the behavior of