How possible is it to break an inmate out during transport?
Having an inmate housed at an outside hospital is the most likely time to have an inmate escape, with or without outside help. During transport is the second most likely time because the escorting staff do not have the physical constraints (fencing, razor wire, fence alarms) of the prison. Hospital staff answering the telephones are not suppose to have any information regarding an inmate being admitted in a hospital but sometimes they do and give it out.
Word gets out to family (or fellow gang members) when an inmate is taken to an outside hospital. There is usually not a lot of choice of hospitals in the range of most prisons. If someone is wanting to help an inmate escape from a public hospital, all they have to do hang around in the hospital lobby during shift change. When they see someone show up in a Correctional Offices's uniform, ride up in the elevator with him and see what floor they get off. Then do some recon later.
The security level of the inmate, the escape risk and the security practices of the prison system will determine how many staff are on duty at the time and if they are armed. Even if they are armed, their weapons are holstered and they are subject to a surprise assault. The risk of escape is at the highest.
Prison staff do their best to not let an inmate or anyone on the outside know when an inmate is going to be taken out for scheduled medical treatments, to court or transferred. Still, the chance for escape is much higher during escorted trips than inside the fences.
Usually the security allocated to a transport is equal to the threat. Also, time, route, and other details, are not public knowledge.