Hi Sara,
The interrupt doesn't transfer the VLPR mode to RUN mode.
Please check below conditions will switch between RUN with VLRP:


Please check if there with code to change the SMC_PMCTRL[RUNM] bits value.
Or there with a reset happens.
BTW:
You could refer MCUXpresso SDK for FRDM-KL03Z SDK package, which provided [power_mode_switch] demo.
I also do a test, there doesn't happen you mentioned issue during debug.
The MCUXpresso SDK for FRDM-KL03Z could be downloaded from here.
Have a great day,
Ma Hui
-----------------------------------------------------------------------------------------------------------------------
Note: If this post answers your question, please click the Correct Answer button. Thank you!
-----------------------------------------------------------------------------------------------------------------------