What do countries do about the physical security of these people, assuming they still don't want to them to come to harm?
They are in jail, so the only people who can "get" them are the other inmates.
The security inside jails is provided by the prison wardens, working under the prison governor. See 'Prison Governance'.
A governor is ultimately responsible for everything that happens within a prison [... including] safety, security and rehabilitation.
For high profile prisoners, or other who may be at greater risk from other inmates (such as sex offenders, particular child abusers) special security arrangements may be made. This could mean isolation from other inmates, or individually tasked wardens. Governors have a duty to keep prisoners safe and secure, and the operational independence to do that.
Not all prisoners are equal in terms of the threat they pose, and so not all prisons are equal. Non-violent prisoners with lower risk of attempted escape are likely to be held under different security conditions from those considered to be more dangerous and more likely to flee.
But the security of prisoners is the responsibility of the Governor, and exercised by the prison wardens and other working for the Governor, such as cooks, office staff etc.