unheilbar
incurable
Describes an illness or condition that cannot be cured according to the current state of medicine.
Leider wurde bei ihm eine unheilbare Krankheit diagnostiziert.
Unfortunately, he was diagnosed with an incurable disease.

incurable
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incurable
Describes an illness or condition that cannot be cured according to the current state of medicine.
Leider wurde bei ihm eine unheilbare Krankheit diagnostiziert.
Unfortunately, he was diagnosed with an incurable disease.

The word is made up of the negation 'un-' and the adjective 'heilbar' (curable). Since 'heilbar' comes from the verb 'heilen' (to heal/cure), 'unheilbar' literally means 'not curable'.
Die Forschung sucht nach Wegen, bisher unheilbare Krankheiten zu behandeln.
Research is looking for ways to treat diseases that have so far been incurable.
In a medical context, 'unheilbar' (incurable) usually stands directly before the word 'Krankheit' (disease) or is used as an adverb with 'krank' (ill). You have an 'unheilbare Krankheit' (incurable disease) or are 'unheilbar krank' (incurably ill).
Er wurde mit der Diagnose konfrontiert, unheilbar krank zu sein.
He was confronted with the diagnosis that he was incurably ill.
In the figurative meaning, 'unheilbar' (incorrigible) describes a fixed character trait. Interestingly, it is often used ironically or affectionately for non-negative traits, for example 'ein unheilbarer Romantiker' (an incurable romantic).
Mein Bruder ist ein unheilbarer Fußballfan; er verpasst kein einziges Spiel.
My brother is an incurable football fan; he doesn't miss a single game.
deadly
'tödlich' and 'unheilbar' can both be used in connection with serious illnesses or injuries. 'tödlich' means that something leads to death or can cause death. 'unheilbar' means that, according to current knowledge, an illness cannot be cured. That does not always have to mean it is immediately or certainly deadly. Learners may confuse the words because both sound very serious. In practice: 'tödlich' describes the consequence, namely death; 'unheilbar' describes the fact that there is no cure.

Beim Arzt erfährt sie, dass die Krankheit unheilbar ist.
At the doctor's office, she learns that the illness is incurable.
Der Unfall war tödlich, obwohl die Hilfe schnell kam.
The accident was fatal, even though help arrived quickly.