The host computer that processes and combines the secondary (transponder) radar data (data block) tags that information to the primary return. If the transponder stops responding to the center's interrogator the data block will coast for a period of time along a presumed track calculated by the host computer.
Whether the primary return remains depends upon whether the aircraft is actually still in a position to be "painted" by the center's primary radar system.
In effect the primary and secondary radar systems are two independent systems.
Data blocks often go into coast for a short period of time without any sinister cause.