Giant 20' x 3' x 2' router build

[JAZZCNC]

for example , when cutting an arc ( as mentioned ) and you stop the machine lets say 1/4 of the way thru the arc , when you restart , it will not resume from that 1/4 point thru the arc ... it will either start at the beginning of the arc , or the next line of G-code

If machine is moving and you hit STOP then you really should presume the machine as lost position and Re-home. If you want to pause the machine and resume then you should use FEEDHOLD.
If machined is STOPPED and you want to resume from point in the G-code then use the RUN from HERE command. This will do a move back into position then pause with message asking for CYCLE START it will also give you option to start the spindle.
If using RUN from HERE then it's best done from the begining of Cycle or some position move in the code rather than half way thru canned drill cycle for instance.
RUN form HERE as saved my arse so many times I've lost count and use it all the time.