Does any scripture say that a Jivanmukta never becomes ill or suffers from any disease?
Those who attain Jivanmukti through Yogic methods, their diseases are all destroyed in an earlier stage only (i.e. much before attaining the Highest Knowledge).
Svetasvatara Upanishad states:
II-12: When the fivefold perception of Yoga, arising from (concentrating the mind on) earth, water, light, air and ether, have appeared to the Yogin, then he has become possessed of a body made of the fire of Yoga, and he will not be touched by disease, old age or death.
II-13: It is said that the first signs of entering Yoga are lightness of body, health, thirstlessness of mind, clearness of complexion, a beautiful voice, an agreeable odour and scantiness excretions.
II-14: Just as the same metal disc, which was stained by dust before, shines brilliantly when cleaned, so the embodied being, seeing the truth of Atman, realizes oneness, attains the goal and becomes sorrowless.
II-15: When the Yogin realizes the truth of Brahman, through the perception of the truth of Atman in this body as a self-luminous entity, then, knowing the Divinity as unborn, eternal and free from all the modifications of Prakriti, he is freed from all sins.
II-16: This Divinity pervades all directions in their entirety. He is the first-born (Hiranyagarbha). He has entered into the womb. He alone is born, and is to be born in future. He is inside all persons as the Indwelling Self, facing all directions.
So, in the stage mentioned in 12 only the diseases are all gone and in 15 knowledge of Brahman is realized. There is no sin at that point, so from where disease will come given that from sins only diseases come?
Yoga Tattva Upanishad states that in the Moksha called Kaivalya, there is no place for any diseases.
- To which Hrisikesha (the Lord of the senses or Vishnu) replied thus: “Listen. I shall explain its truth. All souls are immersed in happiness and sorrow through the snare of Maya. 5-6. Kaivalya, the supreme seat, is the path which gives them emancipation, which rends asunder the snare of Maya, which is the destroyer of birth, old age and disease and which enables one to overcome death. There are no other paths to salvation. Those who go round the net of Shastras are deluded by that knowledge.
And, similarly states the Mandala Brahmana Upanishad ( which is linked with the Sukla Yajurveda):
Through such an absorption, one gets the pure and secondless state, owing to the absence of difference then. This alone is the highest truth. He who knows this, will wander in the world like a lad or an idiot or a demon or simpleton. By practising this Amanaska, one is ever contented, his urine and faeces become diminished, his food becomes lessened; he becomes strong in body and his limbs are free from disease and sleep. Then his breath and eyes being motionless, he realises Brahman and attains the nature of bliss. That ascetic who is intent on drinking the nectar of Brahman produced by the long practice of this kind of Samadhi, becomes a Paramahamsa (ascetic) or an Avadhuta (naked ascetic). By seeing him, all the world becomes pure and even an illiterate person who serves him is freed from bondage. He (the ascetic) enables the members of his family for one hundred and one generations to cross the ocean of Samsara; and his mother, father, wife and children – all these are similarly freed. Thus is the Upanishad.”
So, diseases, old age can not trouble a true Jivanmukta.
A liberated being is liberated only when all their Karmas are completely destroyed. Otherwise liberation or Jivanmukti is not possible.
But, once liberation is achieved, it is said that the Jivanmukta is not affected by any Karmas that he does thereafter. The example often used is that of water can not stay on a lotus leaf, and in similar way sins (or even merits) do not affect the liberated being.
Tattvanishthasya cha karmAni punyApunyAni samkshyam |
PrayAnti naiva lipyante kriyamAnAni vA punah ||
All good and bad Karmas of a Tattva-Nishtha (i.e. self-realized or liberated) person are destroyed and he does not get affected by those even if he performs those Karmas again.
KulArnava Tantram 9.128
Therefore, the liberated beings are already sinless and they can not incur more sins by doing anything. But, diseases are nothing but manifestated forms of accumulated sins.
So, it is easy to see why a Jivanmukta can not be troubled by diseases.