My person is not sure about "on that very day" and sees the "seven days", mentioned in the Suttas more resasonable.
As quoted by Upasaka Saptha Visuddhi in the anicent discussion, the relations within a householder-life, the regards are to weak to supporting, now having perfect virtue, since it's not likely that he may be proper offered what is required to support further life.
My person is also not sure about the saying "must join the order" in a formal sense, but of cause lead a live similar in it's way. Yet it might be "hard" to even get such as robe and bowl, not to speak of being far from people not used, not rejoicing, on special beggars.
It might be that one lives in association with virtuous people who might recognice or know or it might be, that one lives on ten precepts, yet wearing white, since a longer, used to proper live on alms.
How ever, this things are very rare and dhammata, usually, seven days without support might mark the end of the bodies abilities.
The Discussion of Going-forth
(Mv.I.7.12) The money-lender saw Yasa sitting there and on seeing him said to him, “Yasa, my son, your mother is lamenting and full of grief. Give your mother her life (back?)!”
(Mv.I.7.13) Then Yasa looked up at the the Blessed One. Then the Blessed One said to the money-lender, “What do you think, householder: For Yasa, who has seen and known the Dhamma with the knowledge and vision of one in training — just as you have — whose mind, as he reflected on the level (of mind) as he had seen and known it, was through lack of clinging/sustenance released from effluents: Would it be possible for him to revert to the lower life and indulge in sensuality as he did before as a householder?”
“Householder, Yasa has seen and known the Dhamma with the knowledge and vision of one in training, just as you have.
“Reflecting on the level (of mind) as he had seen and known it, his mind was, through lack of clinging/sustenance, released from effluents.
“It would be impossible for Yasa to revert to the lower life and indulge in sensuality as he did before as a householder.”
(Mv.I.7.14) [The money-lender:] “Lord, it’s a gain for Yasa, a great gain for Yasa, that his mind is, through lack of clinging/sustenance, released from effluents!
“May the Blessed One acquiesce to my meal tomorrow, with Yasa as your attendant monk.”
The Blessed One acquiesced with silence.
Then the money-lender, understanding the Blessed One’s acquiescence, got up from his seat, bowed down to him, circumambulated him, keeping him to his right, and left.
(Mv.I.7.15) Then Yasa, not long after the money-lender had left, said to the Blessed One,
“May I receive the Going-forth in the Blessed One’s presence? May I receive the Acceptance?”
“Come, monk.” Said the Blessed One. “The Dhamma is well-taught. Live the holy life.”
Such was the venerable one’s Acceptance. At that time there were seven arahants in the world.
There have been mentions in the text where even Once-returner could not continue ordinary life as usual and starved. My person remembers a young daughter, on hearing the Dhamma been taught, for example.
One may ask: "How comes that one is in such situation?"
Well, it might be the case that there was not much support and nurishment to have the required Upanissaya (strong condition) to have the "luck" being next to the opportunity to go forth. And one might remember that giving food, is the cause of long life.
Outwardly conditions (like food, weather/climate, person/association, dwelling/location) are a matter of upanissayapaccaya, strong condition causes. Having given causes, effects are met.
This to is why wise or faithful lay practing people never fail to invest into a good future, even if not seeing such requirement of the need to have the opportunities to lead the holy life, and give the causes that the/a good Sangha of Bhikkhus is near to them and good maintained.
[Note: This is a gift of Dhamma, given for release, not meant for commercial use or other lower wordily gains by ways of exchange or trade.]