* You persuade your manager that this is okay and name the country.
* BigCo Inc. terminates you and BigCo Lda. or Srl. or whatever there subsidiary in that country makes you an offer letter.
* Your base salary in the new offer is 1/3 less, because "the cost of living" is less. If you ask them if you should do 1/3rd less work, they give you a puzzled look. If you ask them if they discount their prices to customers in low COL countries, they will get mad.
* The non-cash part of your compensation (stock, etc.) should not get impacted much, except that when you get taxed you'll pay more tax. Money isn't everything and you're obviously contemplating this move for other reasons.
* You will accept the offer and follow the immigration procedure of your new country. BigCo will have immigration lawyers they retain to ensure they can hire the candidates they desire, for example you.
* You will chill for a little time, maybe a month, while the immigration process goes through.
* Congratulations, you now have a work visa, benefits, and all the privileges that being a legal employee in that country confer upon you.
Slightly worse are arrangements in which you work through a subcontracting company, don't get benefits, and/or have to fight for the visa yourself.
The other ideas you are contemplating probably don't work, and if you don't understand why you should ask a chatbot not HN.