1) A prisoner cannot collect investment income in jail, but may be able to put the money in the trust of someone else (a family member or friend). Then the other person reports the interest or capital gain income to US Treasury.
2) The prisoner is allowed to file a tax return from in prison, and therefore must do so or be punished the same as another taxpayer.
3) Another person is required to manage the prisoner’s estate.
How does it work?
This certainly applies to white collar prisons.
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I suppose you could authorize someone to handle your personal business matters