Praise be to Allah.
If saliva reaches the lips, then the person swallows it unintentionally, such as if he licks his lips and the like unintentionally, there is no blame on him. Similarly, if it dries up, then he closes his lips, its traces disappear when it dries up, and there is nothing left that could cause one to break the fast at all, whether deliberately or by mistake.
If you deliberately swallow this saliva after it reaches the lips, then there is a difference of scholarly opinion as to whether that breaks the fast.
The Shaafa‘is and Hanbalis are of the view that it does invalidate the fast, because in that case the saliva has separated from where it usually is, which is the inside of the mouth, so swallowing it is like swallowing anything else that is separate from the body.
An-Nawawi (may Allah have mercy on him) said regarding that swallowing of saliva which does not break the fast: Swallowing it from its usual place [does not break the fast], but if it has come out of the mouth, then the person brings it back with his tongue or otherwise and swallows it, it does break the fast.
Our companions said: If it comes out to the outside of the lips, then he takes it back and swallows it, it breaks the fast because it is his fault and because it had left its usual place where it could be overlooked. Al-Mutawalli said: If it came out to his lips, then he took it back and swallowed it, he has broken his fast." (Al-Majmoo‘ 6/342).
Ibn Qudaamah (may Allah have mercy on him) said: If his saliva comes out and gets onto his garment or between his fingers or between his lips, then he takes it back and swallows it, he has broken the fast, because he swallowed it from somewhere other than his mouth, so it is like swallowing anything else." (Al-Mughni 3/17).
The Hanafis are of the view that it does not invalidate the fast unless it becomes separate from the mouth, then he takes it back into his mouth.
It says in Fath al-Qadeer (2/332): If his saliva came out of his mouth, then he took it back in and swallowed it, if it did not become separate from his mouth – rather it remained connected to what is in his mouth, like a thread, and he took it in and swallowed it – he has not broken his fast. But if it became separated, then he took it back, he has broken his fast, but he does not have to offer any expiation, such as if he swallowed someone else’s saliva, or if it collected in his mouth then he swallowed it; that is makrooh, but it does not break the fast. End quote.
You should be careful with regard to the saliva that accumulates on the mask and becomes separate from the mouth. So do not deliberately take it back into the mouth and swallow it.
Regarding that which is difficult to avoid or enters the mouth without you intending it to, that is most likely to be overlooked, because it is a small amount and difficult to avoid. The Lawgiver overlooks traces of water that remain in the mouth after rinsing it [when doing wudoo’].
If you do not know whether it entered the mouth again or not, it is more appropriate to disregard it, because the basic principle is that you have not broken the fast, and that the saliva has not returned to the mouth.
And Allah knows best.