When you achieve nirvana , you have given up yourself. There is no person anymore. But my question is , if someone says publicly that he is arahant, is there a possibility that it can be true?
From a Theravada perspective, the answer is probably "no".
While not being a sutta, the Milindapanha states if a layperson attains to Arahatship they either ordain as a monk or die.
If the layperson Arahant ordains as monk, the Vinaya forbids them making a public declaration.
Should any bhikkhu report (his own) superior human state to an unordained person, when it is factual, it is to be confessed.
As for the Buddha & monks that declared arahantship in the Pali suttas, if they used the personal pronoun "I", they were only speaking in conventional language. Refer to SN 1.25.
Maybe it's not possible for an arahant that is a monastic, because it is appropriate for monastics to follow the monastic rules (which discourage saying such a thing in public).
An arahant has no attachment to ego so it isn't as though a lay arahant's public proclamation of enlightenment would cause the arahant any bad karma. An arahant would need an appropriate reason to make such a claim though. Maybe there could never be an appropriate reason to make such a claim; or maybe there could be an appropriate reason, as simple as someone asking the arahant, "How's your meditation practice going"?
Buddha has said that an Enlightened person doesn't go and cling with the self. So they don't have any attachment to self. But a inAn10.92` the Buddha has clearly mentioned the following.
Then Anathapindika the householder went to the Blessed One and, on arrival, having bowed down to the Blessed One, sat to one side. As he was sitting there, the Blessed One said to him, “When, for a disciple of the noble ones, five forms of fear & animosity are stilled; when he is endowed with the four factors of stream-entry; and when, through discernment, he has rightly seen & rightly ferreted out the noble method, then if he wants he may state about himself: ‘Hell is ended; animal wombs are ended; the state of the hungry shades is ended; states of deprivation, destitution, the bad bourns are ended! I am a stream-winner, steadfast, never again destined for states of woe, headed for self-awakening!’
So an Enlightened person, can say that I'm enlightenment to another person for the sake of showing that person the path of enlightenment
Depends on the achievement of nirvana, either monk or not, in case of sotapanna, sakadagami, anagami,arahant, if they say with good intention, it is ok referring to Thera Theri Apadana. GOOD INTENTION means not for fame, not for offerings , only for the laymen to follow the proper path of Magga and attain nirvana.
Why not? "Off (good) cause" there are reasons why not and on (good) course reasons why.
It's rather foolish to say that an awakened would not share past merits if conuctive or would anybody saw the Buddha him self lived a paradox?
Since an Arahat (especially) would not "claim" such for certain low puposes, not to speak of evil, he might not violate even a precept or rule (how could he?)
For example a clear indication that such sharing of merits are not bad at first hand but has rather to do with generaly issa in certain communities believing equanimity is the highes virtue:
Then Anathapindika the householder, surrounded by about 500 lay followers, went to the Blessed One and, on arrival, having bowed down to him, sat to one side. So the Blessed One said to Ven. Sariputta: "Sariputta, when you know of a householder clothed in white, that he is restrained in terms of the five training rules and that he obtains at will, without difficulty, without hardship, four pleasant mental abidings in the here & now, then if he wants he may state about himself: 'Hell is ended; animal wombs are ended; the state of the hungry shades is ended; states of deprivation, destitution, the bad bourns are ended! I am a stream-winner, steadfast, never again destined for states of woe, headed for self-awakening!'1 ...Gihi Sutta: The Householder
[Feel personal always invited to share such merits here: "Ich bin ein Stromgewinner!" - "I am a stream-winner!"]
A maybe extended answer and also further questions and discussion can be done and found here: [Q&A] If someone says publicly that he has achieved nirvana , can it be true ?
(Note: This is a gift of Dhamma and not meant for commercial use or other purposes for wordily gains.)
No one can declare that one cannot say he/she has achieved nirvana. Didn't lord Buddha declare that he achieved nibbana? If some one has achieved nirvana don't he/she has to declare it to others in order to teach them about the correct path to nirvana? If you say 'no', then how can he/she guide others to the nirvana? Thus it will depend on the person whether to declare it on public or not. No one can thoroughly say 'no'.