If a person fasts for a Kaffarah and during the day their lips cracked and started to bleed. The person put their tongue on their lip and tasted the blood. But this was not intentionally. Does this break their fast? Or do you think that they should do their Kaffarah again?
Technically, yes this is an issue (but there is a loophole of some sorts). It has happened to me before, and so I had decided to confront one of the Marja' about this (Makarem Shirazi).
What he told me is that in fasting, the "rule" is that you cannot drink any liquids nor eat anything. Blood is a liquid, and thus does nullify the fast if goes into your mouth. HOWEVER, if the blood goes into your mouth without you noticing it, and when you do notice it you immediately wipe the blood off your lips to make sure it does not enter your mouth again, this is considered legal.
Hopefully this helps you.