In his Tafsir al-Kashif volume 1 page 407, Allamah Muhammad Jawad Mughniyah (may Allah bless him) discusses the punishment which a dead person receives in the grave. The author divides mankind into four groups. I request you to throw some light on those four groups especially the third and the fourth ones.
When it comes to the third group of people, Shaykh Mufid (r.a) describes them as doubtful. What is meant by 'doubtful' here? As for the fourth group, he says that they are dead and they will remain dead until the Day of Resurrection. Kindly, explain the fourth group of people as to who they are? Shaykh Mufid uses as evidence a tradition from the Infallible Imams who said: "Some of the dead people are not punished in the graves."
In his book Awael al-Maqalat, Shaykh Mufid sorts out human individuals based on their beliefs and deeds into four groups:
1. Pious believers;
2. Disbelieving, stubborn and grudging sinners;
3. Believers who have committed major sins and not done Tawbah. They are people who have not committed sins out of grudge and stubbornness; rather they have committed sins on account of their being under the influence of their whims and carnal desires.
4. Those who lack the luminous inner vision and precise religious understanding (Mustaz'afin) irrespective of whether they are apparent believers or unbelievers.
Given that Shaykh Mufid (r.a) had access to religious sources and references, he had reached a decisive conclusion as to the first, second and fourth group. Therefore, he held that the first and second groups have a barzakh life (between death on Earth and resurrection) – albeit one in divine bounty and the other in punishment.
The fourth group of people also does not have a barzakh life according to him but he has not reached a clear and decisive conclusion in regards to the third group. That is why he has given some probabilities and has, with uncertainty, described the third group as 'doubtful'.
There is a verse in the holy Quran which explicitly states that there is an intermediate world (Barzakh) between death and resurrection. There are other examples in the Quran in which it speaks of or describe people who have passed away from the world and who have not yet reached the Day of Resurrection. These verses indicate that there is an intermediate world called "Barzakh".
There are many narrations in Shiite and Sunni sources which describe the intermediate world with more precise details.
Based on the above, the existence of an intermediate world is unquestionable but there is a difference of opinion as to the specific features of this world; different Muslim scholars have provided varying details in their analysis.
Avael ul Maqalat is also a book authored by Shaykh Mufid, one of the prominent Shiite scholars of the fourth and fifth century of the Islamic calendar. He wrote the book in response to various questions and queries on ideological subjects including the intermediate world. Naturally, the inferences made by him with reliance on the verses and traditions are those of him, not of the entire Shiite community.
Having said that, now we return to your question, and we will follow what you have quoted from Tafsir al-Kashif through Avael ul Maqalat of Shaykh Mufid – may Allah bless him.
In this book, Shaykh Mufid accepts the intermediate world in a general way and describes the situation of people therein. He says: We can study the situation of people in the intermediate world under one of the following four groups:
The first group of people is those who are alive enjoying divine bounties and living in close proximity to the imams. The second group of people is those who are alive and are being chastised. There is a third group of people also about whom we have no precise information nor have we come to a certain conclusion about the way they are living. Basically, we are not sure if they are having an intermediate life. Finally, the fourth group of people includes those people who do not have an intermediate life and that they are numb and dead in the period between this world and the hereafter.
Shaykh Mufid (r.a) then goes on analyzing the above four groups one after another:
1. Those people who have complete inner vision of themselves in the world and are fulfilling their divine obligations in proper manner shall be alive and shall benefit from the bounties bestowed upon by them by the Lord.
2. There are some people in this world who do not embrace the true religion on account of grudge and stubbornness. Such people who have the ability to know the truth or know it and still oppose it for the sake of material worldly benefits and continue to commit major sins are alive in the intermediate world. Unlike the first group, they have a life fraught with anguish, agony and punishment.
3. There are also some people who despite believing in the right religion commit great sins. In fact, they do not commit sins owing to grudge and stubbornness or because they consider them as permissible; rather they commit sins on account of their being overpowered and overcome by their whims and carnal desires. What would be their situation like in the intermediate world, if they fail to repent before death?
Thereupon, Shaykh Mufid (r.a) says: We do not know as to how their situation in the intermediate world is as we maintain doubt about the destiny Almighty Allah has set for them. It is likely that:
1 – 3. God, the Exalted, may keep them alive in the intermediate world and subject them to punishment so that they may, after getting the punishment in the grave and in the intermediate world, be purified and go to Paradise.
2 – 3. This group of people has no intermediate life and that they will be held responsible for their deeds on the Day of Judgment. God, the Exalted, will deal with them and consider some of them to be liable to punishment in Hell and some others as worthy of forgiveness and mercy.
Finally, Shaykh Mufid (may Allah bless him) concludes that in spite of having access to the Quranic verses and also traditions, he could not have verified the situation of the third group. He says that God, the Glorified, may have wanted to conceal their situation from us.
4. There are two other groups of people one of which includes apparently faithful people who do not have the least understanding and insight about religion, and the other includes unbelievers whose disbelief in the right religion is not because of grudge and stubbornness but because of lacking access to a proper cultural atmosphere and to the means of understanding. In other words, they are suffering from cultural poverty and weakness. According to Shaykh Mufid (r.a), these two groups of people do not have an intermediate life and that they are numb and dead in the period between this world and the hereafter.
To get a summery of what Shaykh Mufid believes in, we request you to read the "General Answer" once again. Meanwhile, we should reiterate that the above classification and the inferences made by Shaykh Mufid with reliance on the verses and traditions are those of him, not of the entire Shiite community. Therefore, other Shiite scholars may have other juridical views in this regard.
Also, there are other questions and answers available on this website concerning Barzakh (the intermediate world) which you can refer to and read for further information.
 - Al-Momenoon, 100, "و من ورائهم برزخ إلی یوم یبعثون".
 - Aal-e Imran: 169 – 171; Yasin, 26-27.
 - See: Majlisi, Muhammad Baqir, Behar al-Anwra, vol.6, pg.202 onward, Al-Vafa Insititute, Beirut, 1401 A.H; Qurtubi, Al-Jame' le-Ahkaam al-Quran, vol.13, pg. 150, Intisharat Naser Khosro, Tehran, 1985.
 - Shaykh Mufid, Avael ul Maqalat, p.g75 – 76, Congress on Shaykh Mufid (r.a), Qom 1413 A.H.
 - See: questions 3891, (site: 4160), 3813 (site: 4283), 4905 (site: 5648).