Isn't that the case only when country A is the USA? AFAIK, nearly all countries in the world tax only residents, not citizens, so in most cases you'd only have to fill tax paperwork (and pay taxes) for country B.
And since you are now filling in two tax returns for different countries, with different tax allowances across rental income and work income which interact in decidedly non-linear fashion, you probably need to make sure both country A and B have no confusion about where your work income was earned.
Having spent the last 8 years obsessively counting days across the UK and Finland (and every other country I have visited) exactly to account for this scenario, I am very sympathetic to attempts to solve this problem space!
But then, that's because you own property in country A, not because you're a citizen of country A! The same would happen if you were a citizen of country B, lived and worked in country B, but bought a house to rent out in country A.