There are two possibilities:
1) the country in question is engaged in AEOI/CRS system (Sweden is);
or
2) the country in question is NOT engaged in AEOI/CRS system.
If (1), then at the end of every year the financial information about you is automatically shared; if (2), then nothing is shared automatically but it usually can be shared on request (practically all countries agreed with this nowadays).
For a list︀ of non-AEOI/CRS coutries, you can search OECD website or even threads here.
USA are the︁ special case because they are not in AEOI but have FATCA. The result is a︂ little bit more complicated but generally you can treat it as relatively safe for non-US︃ citizens and unsafe (i.e. shared) for US citizens.