Inmates in prison can have shoelaces in prison as long as they are not on suicide watch or put into isolation inside of the prison.
If they are not a high risk prisoner or on suicide watch or in isolation or solitary confinement then the inmate is allowed to have shoelaces.
Some prisoners wear prison shoes without shoelaces and some prisoners wear shoes that have shoelaces.
It depends on the security of the prison and prison inmate.
However in jail you wear jail sandals and are not allowed to wear any shoelaces.
Once you go to prison depending on the prison you serve your time at you may or may not be allowed shoelaces.
If you're on suicide watch, death row, etc then you won't be allowed to have shoelaces.