In the 1970s and earlier, prisoners were able to receive Social Security benefits. However, nowadays, people convicted of a crime and doing time in prison in general can not receive Social Security benefits.
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Or to be more precise, benefits are suspended if someone is convicted of a criminal offense and sent to jail or prison for more than 30 continuous days. Notice that conviction is the key. Lots of people end up in jails while they are awaiting trial or pleas. But until there is a conviction with prison time involved, benefits will continue.
However, if the convict has a dependent who's receiving Social Security benefits who is not in jail, those dependent benefits can continue.
Also, note prisoners may not receive SSI benefits either.