There is no cost to receive text messages (SMS) while abroad,
so as long as your local SIM card is active, you can continue receiving SMS messages as usual — even when you're outside your home country.
However, if your SIM card is not active (for example, if you removed it from the device or there is no signal), you won’t be able to receive SMS to your original number — only voice calls, which will be forwarded through the KeepMyNumber app.