Switching my phone provider to one I can use abroad

Hi all – I have lived here for 10+ years and have kept the same number the entire time. My entire life is attached to this phone number thanks to 2 factor authentication. I use LINEMO (not the new Lineモバイル). I travel a lot, and have realised that even when I turn the sim on, allow for data roaming etc I cannot receive messages to the number, it seems to work within Japan only.

I'm planning for an exit, but want to keep this number as my exit will likely be temporary only. Can you please recommend a cheap provider that I can move to which will allow for me to receive messages when abroad? I say cheap as I won't really be using the number/ data otherwise. It would just be for when I am abroad and need to get my 2fa codes, and likely will have another number in the country I move to that I'd need to pay for separately.

Thanks!