It would appear that we have to distinguish between a person who is قاصِر (qaasir=weak and helpless) and one who is مقصِّر (muqassir=negligent) Qaasir is one who is weak and helpless, which can be either due to the truth not getting to him, such that he does not find out about the true Islam - as per the example given above, or that he is in a situation such that he cannot get away from it e.g. his passport is taken away and is therefore unable to leave the country.
A Muqassir is one to whom truth is accessible but is negligent about it, or when exposed to it, denies it.
The Qur'an describes these two conditions using the word "مستضعفین " (mustadh'afeen=weak and miserable).
In surah Nisa, verses 97, we read: اِنًّ الَّذِينَ تَوَفَّاهُمُ الْمَلائِكَةُ ظالِمِي أَنْفُسِهِمْ قالُوا فِيمَ كُنْتُمْ؟ قالُوا كُنَّا مُسْتَضْعَفِينَ فِي الْأَرْضِ، قالُوا أَ لَمْ تَكُنْ أَرْضُ اللَّهِ واسِعَةً فَتُهاجِرُوا فِيها؟ فَأُولئِكَ مَأْواهُمْ جَهَنَّمُ وَ ساءَتْ مَصِيرا
Indeed, those whom the angels take away while they are wronging themselves, they ask," What state were you in?" They reply," We were abased in the land." They say," Was not Allah's earth vast enough so that you might migrate in it?" The refuge of such shall be hell, and it is an evil destination. (97)
In this verse, there is a dialogue between the angels carrying out Allah's commands and some of the people after their death. When the angels asked them about their life in the world, they excuse themselves by saying 'we were abased (ie weak) in the land. From the answer of the angels to this excuse we understand that their excuse is lame and not acceptable. They are not weak. They are muqassir and negligent. Therefore they should be punished.
The following verse, 98: إِلَّا الْمُسْتَضْعَفِينَ مِنَ الرِّجَالِ وَ النِّسَاءِ وَ الْوِلْدَانِ لَا يَسْتَطِيعُونَ حِيلَةً وَ لَا يهَْتَدُونَ سَبِيلا
Except the abased among men, women and children, who have neither access to any means nor are guided to any way. (98)
This verse is pointing to those people who are really weak in the land, unable to flee from oppression. These people are qaasir and the real 'mustadh'afeen' and weak in the land. These will not be punished. So what will be their fate?
The following verse explains: فَأُوْلَئكَ عَسىَ اللَّهُ أَن يَعْفُوَ عَنهُْمْ وَ كاَنَ اللَّهُ عَفُوًّا غَفُورًا
Maybe Allah will excuse them, for Allah is all-excusing, all-forgiving.(99)
For the real weak in the lands, there is hope that the Merciful Lord will excuse and forgive them.
Allama Tabatabai in the tafsir of these verses, says that just like it is possible the cause of the weakness in the lands is the inability to change environment and seek better pastures, it is also possible that the human mind has not been exposed to the truth therefore being deprived from the truth - a clear example being the south american tribe. The muqassir include those to whom the truth was available but were negligent and did not go towards it, or even denied it.
It can be concluded from the Qur'an (and ahadith of the ma'sumeen) that the qaasir and weak will not be punished in the next world.
For further reading, Divine Justice of Shaheed Mutahhari is suggested.