ausfallen
to be canceled
To not take place; to be canceled.
Wegen Krankheit des Lehrers fällt der Unterricht heute aus.
Because the teacher is sick, class is canceled today.

to be canceled / to fail
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to be canceled
To not take place; to be canceled.
Wegen Krankheit des Lehrers fällt der Unterricht heute aus.
Because the teacher is sick, class is canceled today.

'Ausfallen' (to be canceled / to fail) is a separable verb. The prefix 'aus-' goes at the end in main clauses; in subordinate clauses and in the infinitive with 'zu', the verb stays together.
Der Zug nach Berlin fällt heute aus.
The train to Berlin is canceled today.
The perfect tense of 'ausfallen' (to be canceled / to fail) is always formed with the auxiliary verb 'sein' (to be), because it describes a change of state. So the form is 'ist ausgefallen' (has been canceled / has failed).
Die Heizung ist mitten im Winter ausgefallen.
The heating failed in the middle of winter.
The context reveals the exact meaning. If the subject is an event or an appointment, it means 'not take place'. If the subject is a technical device or system, it means 'no longer function'.
Die morgige Vorlesung fällt aus.
Tomorrow's lecture is canceled.
In the meaning 'to have a result', 'ausfallen' (to turn out) is almost always accompanied by an adverb or adjective that describes the quality of the result.
Der Test ist besser ausgefallen als erwartet.
The test turned out better than expected.
When hair or teeth fall out, the affected person is often named with a dative object. The subject of the sentence is the thing that falls out.
Dem alten Hund fallen langsam die Zähne aus.
The old dog's teeth are slowly falling out.
to lose
'verlieren' and 'ausfallen' can both refer to hair or teeth no longer being there. 'ausfallen' describes the process: a hair or tooth comes loose from the body and falls out. 'verlieren' describes more the result or the general loss: someone has less hair or no longer has a tooth. The words can therefore easily be confused. With hair, people often use both, but 'ausfallen' is more precise for the natural or physical process.

Bei meinem kleinen Bruder ist gestern der erste Zahn ausgefallen.
My little brother's first tooth fell out yesterday.
Nach der Krankheit hat sie viele Haare verloren.
After the illness, she lost a lot of hair.