We typically use overload relays in parallel. A typical single-line diagram for a motor control centre (switchboard which supplies motors) is shown below.
The principle is: A fault on one motor should not affect the rest of plant, unless it's critical to the operation of the overall process.
I've never seen motor overload relays used in series.
If a fault on a motor does affect the overall process, we'd use an auxiliary contact of the overload relay to create an interlock.
For example, a large motor might need a grease pump to maintain lubrication to its bearings. If the grease pump stops working, we need to stop the motor. We would do this by taking an auxiliary contact off the grease pump's overload relay, and wiring it into the starter circuit for the large motor. This way, if the grease pump suffers a fault, the auxiliary contact will drop out, and the large motor will stop.