As I understand it, if someone protected by the Secret Service were to be sentenced to jail or prison time, the Secret Service would pass protective duties on to the agency or institution handling the incarceration. It's equivalent, in effect, to the way that convicted prisoners are already formally transferred between police, court bailiffs, sheriffs, and prison staff as they move through the legal system. There's paperwork involved, but not much else.
In other words, the Secret Service would handle protective details up until the person in question was convicted (or incarcerated pending trial), and then would hand that person over to the incarcerating authorities with certain guarantees: most likely periodic inspections and reports, and limitations on the convict's exposure to other prisoners. The person in question would not receive Secret Service protection while in custody, because that duty would fall on the custodial authority. There's nothing special about Secret Service protection — it's a police agency like any other — so once the convict passes into the locus of control of a different agency, the Secret Service will cede most of its responsibilities to that other agency.
I know this is an unprecedented case, but bureaucracy has its own irrefutable logic that is unlikely to be denied.