Hi @hilary_stoupa,
I have made a test on my side, if you add a "Start an approval" action to send an approval email within your flow, then you turn off this flow when the flow is running, this flow run would keep running until the approver makes a response to this approval request or the "Start an approval" action times out.
There is a limitation in the Run duration of a single flow run, the max Run duration of a single flow run is 30 days. After 30 days, if the approver still doesn't make a response to this approval request, the "Start an approval" action would time out.
More details about the limits in Run duration and retention of a single flow run, please check the following article:
Run duration and retention
Best regards,
Kris