The vast majority of us will never encounter such a scenario but...
Outside of asking a family member/friend to retrieve your HW wallet and/or seed
What do you do in such a scenario?
While it's generally not recommended, IMO this one of scenario where brainwallet or having encrypted cloud backup may help you.
Still not recommended like you said, cloud backup have messed many people up, I will only do this if the amount of the total asset isn't that much, in the hundreds of dollars, the moment it's over a thousand in dollars it is best to buy a hardware wallet, how you want to move it around is your problem.
I'm aware cloud storage doesn't always have good reputation due to them prevent user access their data or closed it service. But the risk could be reduced by using multiple cloud storage provider.
Honestly this isn't the advice we should be sharing base on what OP shared, instead of saying that brainwallet or cloud backup isn't generally bad in this type of situation why can't we advice people to stay away from crime, any type of crime that can get you deported from a foreign country abstain from it.
OP labeled her, the old woman as ordinary, I refuse to believe it, it is nothing out of the ordinary that some people are doing everything they can to survive in today's world, these people can't be clean and still get deported, ordinary residents? They are not ordinary.
OP clearly ask how to keep having access to Bitcoin in such scenario, rather than preventing such scenario. I won't debate whether the deportation (along with asset confiscation) is justifiable or not.
I see a lot of people talking about brainwallet or having encrypted cloud backup, using these is the same as using an exchange.
Brainwallet basically works by hashing text into 256-bit data which as private key, so saying brainwallet is same with using exchange is ridiculous. As for encrypted backup on cloud storage, the cloud storage provider doesn't have access to your Bitcoin either (unless they decide to copy and decrypt it).