Answer
✅ Answer: In Shi'a narrations, there is no prohibition on their remarriage, unless, according to the hadiths, the woman is obligated to observe the 'Iddah period. All encouragements to marry and condemnations of remaining single also apply to these individuals.
As an example of the tradition in this regard, pay attention to a part of the will of Fatima Zahra (peace be upon her) to the Commander of the Faithful (peace be upon him):
یَا ابْنَ عَمِّ رَسُولِ اللَّهِ أُوصِیکِ أَوَّلًا أَنْ تَتَزَوَّجَ بَعْدِی بِابْنَةِ أُخْتِی أُمَامَةَ فَإِنَّهَا تَکُونُ لِوُلْدِی مِثْلِی فَإِنَّ الرِّجَالَ لَا بُدَّ لَهُمْ مِنَ النِّسَاءِ قَالَ فَمِنْ أَجْلِ ذَلِکَ قَالَ أَمِیرُ الْمُؤْمِنِینَ أَرْبَعٌ لَیْسَ لِی إِلَی فِرَاقِهِ [ فراقهن] سَبِیلٌ بِنْتُ أَبِی الْعَاصِ أُمَامَةُ أَوْصَتْنِی بِهَا فَاطِمَةُ بِنْتُ مُحَمَّدٍ ثُمَّ قَالَتْ أُوصِیکَ یَا ابْنَ عَمِّ أَنْ تَتَّخِذَ لِی نَعْشاً فَقَدْ رَأَیْتُ الْمَلَائِکَةَ صَوَّرُوا صُورَتَهُ فَقَالَ لَهَا صِفِیهِ لِی فَوَصَفَتْهُ فَاتَّخَذَهُ لَهَا فَأَوَّلُ نَعْشٍ عُمِلَ عَلَی وَجْهِ الْأَرْضِ ذَاکَ وَ مَا رَأَی أَحَدٌ قَبْلَهُ وَ لَا عَمِلَ أَحَدٌ ثُمَّ قَالَتْ أُوصِیکَ أَنْ لَا یَشْهَدَ أَحَدٌ جِنَازَتِی مِنْ هَؤُلَاءِ الَّذِینَ ظَلَمُونِی وَ أَخَذُوا حَقِّی فَإِنَّهُمْ عَدُوِّی وَ عَدُوُّ رَسُولِ اللَّهِ ص وَ لَا تَتْرُکُ أَنْ یُصَلِّیَ عَلَیَّ أَحَدٌ مِنْهُمْ وَ لَا مِنْ أَتْبَاعِهِمْ وَ ادْفِنِّی فِی اللَّیْلِ إِذَا هَدَأَتِ الْعُیُونُ وَ نَامَتِ الْأَبْصَارُ...
📚 Bihar, Vol. 43, p. 192
Translation: Fatima Zahra (peace be upon her) in her will to the Commander of the Faithful (peace be upon him) said, among other things: 'O son of the Messenger of Allah's uncle, first I advise you to marry my sister's daughter, 'Umama bint Abi al-'As,' after me, because she will be like me for my children, for indeed men are inevitably in need of women.' For this reason, the Commander of the Faithful (peace be upon him) used to say: 'There are four things from which I have no way of separating!' (One of them is) marrying Umama bint Abi al-'As, because Fatima, the daughter of Muhammad (peace be upon him and his family), willed me to marry her. Then Fatima (peace be upon her) said: 'O son of my uncle! I advise you to make a coffin for me that the angels showed me the shape and form of.' Ali (peace be upon him) said: 'Describe its characteristics to me,' and Fatima (peace be upon her) described it, and the Commander of the Faithful (peace be upon him) made that coffin for her (so that the volume of her body would not be visible), and this type of coffin was the first coffin that was made on earth, and no one had seen or made one before it. Then she said: 'I advise you that no one from among those who oppressed me and took my right should be present at my funeral, for they are my enemies and the enemies of the Messenger of Allah (peace be upon him and his family). And do not let any of them or their followers pray over my funeral. And bury me at night when the eyes have settled and the sights have gone to sleep...'
✅ Also, in the hadith from 📚 Al-Kafi, Vol. 6, p. 113, Imam Jawad (peace be upon him) said about the reason for the four-month duration of 'Ila':
فَلَمْ یُجَوِّزْ لِأَحَدٍ أَکْثَرَ مِنْ أَرْبَعَةِ أَشْهُرٍ فِی الْإِیلَاءِ لِعِلْمِهِ تَبَارَکَ اسْمُهُ أَنَّهُ غَایَةُ صَبْرِ الْمَرْأَةِ عَنِ الرَّجُلِ
Meaning: 'Allah has not allowed anyone more than four months in 'Ila', because Allah knew that the maximum a woman can endure from a man is four months...'
And he also said about the reason for the four-month and ten-day duration of the 'Iddah of death:
وَ عَلِمَ أَنَّ غَایَةَ الْمَرْأَةِ الْأَرْبَعَةُ أَشْهُرٍ فِی تَرْکِ الْجِمَاعِ
Meaning: 'Allah knew that the maximum duration (of a woman's endurance) in leaving... is four months...'
✅ Note: 'Ila' is when a man swears an oath to abandon his wife to cause her distress. It has detailed rulings that are mentioned in their own place.
اللَّهُمَّ صَلِّ عَلَی مُحَمَّدٍ وَ آلِ مُحَمَّدٍ وَ عَجِّلْ لِوَلِیِّکَ الْفَرَجَ وَ الْعَافِیَةَ وَ النَّصْرَ