Exile to Sado Island - How does it work?

RPG related question for an Alt-History campaign set on the eve of
the Onin War... I'll have more questions if this proves useful.

I have read that a wide variety of noted worthies were all exiled to
Sado Island, apparently to work in mines or something. I also note
that it was considered a one way trip. How does that work, exactly?
I see that it was ruled by the Homma clan for the relevant period.
Did they act as jailers for the court and Shogunate? Did only people
that it was impolitic to execute get sent there?

I have the following hypothetical examples in my mind's eye:

#1 "Prince Okisugi no Guchi offends the Emperor one too many times
with his scandalous gossip, and he is ordered to relocate to Sado
Island. His estates forfeit, the prince is escorted by a retinue of
Imperial guardsmen across Japan, taking only what his four or five
servants will carry. After many weeks of travel, during which he is
given opportunities to end his own life with dignity, he is loaded
onto a boat and transferred to Homma custody, where he is received as
an honored guest... meaning he lives out his days in a decrepit
seaside house with one loyal servant, writing his memoirs. He does
not escape, because if he does, he will be executed, or something bad
might happen to his relatives in Kyoto, or his considerable remaining
dignity will be squandered. "

#2 "Priest Yominikui offends the Shogun one too many times with his
atrocious poetry. It is considered bad form to kill a priest who is
distantly related to Lord Yamana Sozen, so he is instead slapped in
chains, carted to the boat, and shipped to Sado Island. There he is
far too busy digging in the Homma silver mines to write poems. Priest
Yominikui eventually expires under the strain of his new labors."

Would it be plausible for PC's to be sent to Sado by a powerful
patron to retrieve some old noble, because he was needed for the
brewing Onin intrigues? Or perhaps simply for a PC to carry a private
letter from one powerful person to an exiled Imperial relative,
seeking support for some power play?

Thanks,
Andrew