We have quite a few narration which say that the believer seems the Imam's (as) on his death bed.

Hadith 1:

النضر بن سويد عن يحيى الحلبي عن عبد الحميد الطائي قال:سمعت أبا عبد الله عليه السلام يقول إن أشد ما يكون عدوكم (كراهة) (كراهته) لهذا الامر إذا بلغت نفسه هذه وأشد ما يكون أحدكم اغتباطا به إذا بلغت نفسه هذه - وأشار إلى حلقه - فينقطع (فتقطع) عنه أهوال الدنيا وما كان يحاذر عنها (فيها) ويقال له: امامك رسول الله صلى الله عليه وآله وعلى والأئمة عليهم السلام

Narrated through a chain of reliable/trustworthy narrators that Abu Abd-Allah Imam Sadiq (عليه السلام) said,

"The most intense state in which your enemy can happen to be in while hating this matter (i.e., Wilayah) is when his soul reaches here (throat), and the most intense state of happiness/delight in which one of you (Shias) can happen to be in is when his soul reaches here – and the Imam gestured to His throat – Then the horrors of the world will be cut off from him, and what he used to be wary/afraid of in the world. And it would be said to him, "In front of you is the Prophet of Allah (صلى الله عليه وآله), and Ali (عليه السلام), and the Imams (عليهم السلام)."

[Source: Kitab al-Zohad, Pg. 84, Hadith. 224]

Hadith 2:

حماد بن عيسى عن حسين بن المختار عن أبي بصير عن أبي عبد الله عليه السلام أنه قال: إن المؤمن إذا مات رأى رسول الله صلى الله عليه وآله وعليا عليه السلام بحضرته

Narrated through a chain of reliable/trustworthy narrators that Abu Abd Allah Imam Sadiq (عليه السلام) said, 

"Verily the dead when he dies sees the Prophet (صلى الله عليه وآله) and Ali (عليه السلام) in his presence."

[Source: Kitab al-Zohad, Pg. 84, Hadith. 225]

Hadith 3:

محمد بن يحيى، عن أحمد بن محمد بن عيسى، عن ابن فضال، عن يونس بن يعقوب، عن سعيد بن يسار أنه حضر أحد ابني سابور وكان لهما فضل وورع و إخبات فمرض أحدهما وما أحسبه إلا زكريا بن سابور قال: فحضرته عند موته فبسط يده ثم قال: ابيضت يدي ياعلي، قال: فدخلت على أبي عبدالله (عليه السلام) و عنده محمد بن مسلم قال: فلما قمت من عنده ظننت أن محمدا يخبره بخبر الرجل فأتبعني برسول فرجعت إليه فقال: أخبرني عن هذا الرجل الذي حضرته عند الموت أي شئ سمعته يقول؟ قال: قلت بسط يده ثم قال: ابيضت يدي ياعلي، فقال أبوعبدالله (عليه السلام): والله رآه، والله رآه، والله رآه.

Narrated by Muhammad bin Yahya, from Ahmad bin Muhammad bin Isa, from Ibn Fazzal, from Younus bin Yaqob, from Saeed bin Yasir:

That I was there when one of the sons of Ibn Saaboor, who was a pious and great man, was ill, and i think his name was Zakariya bin Saabor, so at the time of his death, he extended his hand, and said, "You have enlightened my hand O Ali!"

The Narrator said, when I met Abi Abdillah (as) and Muhammad bin Muslim was also with him.

He (narrator) said: when I stood up from him, I believe mohammad bin muslim had told him about that man. So his Messenger came and I went with him to him.

Imam (as) said, "Tell me about this man with whom you were at time of his death, what did you hear? He said: I said he extended his arm and said that you have enlightened my hand O Ali.

So Abi Abdillah (as) said: By God! He saw Him,  By God! He saw Him , By God! He saw Him.

[Source: Al-Kafi, Vol. 3, Pg. 131]

Narration is Realiable as per chain of narrators. See Mirat-Al-Uqool - Allama Majlisi, Vol. 13, Pg. 289

Hadith 4:

أخبرنا محمد بن محمد، قال: أخبرنا أبو القاسم جعفر بن محمد بن قولويه، قال: حدثنا أبو علي محمد بن همام، قال: حدثنا علي بن محمد بن مسعدة، قال: حدثني جدي مسعدة بن صدقة، قال: سمعت أبا عبد الله جعفر بن محمد (عليهما السلام) يقول: والله لا يهلك هالك على حب علي (عليه السلام) إلا رآه في أحب المواطن إليه، والله لا يهلك هالك على بغض علي (عليه السلام) إلا رآه في أبغض المواطن إليه

Narrated that Abu Abd-Allah Jafar bin Muhammad (عليه السلام) said,

"By Allah (عز وجل), the one who loves Ali ibn Abi Talib (عليه السلام) does not dies until he sees Him in the places most beloved/desirable to him. And by Allah (عز وجل) the one who hates Ali ibn Abi Talib (عليه السلام) does not die until he sees Him in the places most hateful to him"

[Source: Amaali - Sheikh Tousi, Pg. 164]

Hadith 5:

مُحَمَّدُ بْنُ يَحْيَى عَنْ أَحْمَدَ بْنِ مُحَمَّدٍ عَنْ عَلِيِّ بْنِ الْحَكَمِ عَنْ مُعَاوِيَةَ بْنِ وَهْبٍ عَنْ يَحْيَى بْنِ سَابُورٍ قَالَ سَمِعْتُ أَبَا عَبْدِ الله (عَلَيْهِ الْسَّلام) يَقُولُ فِي الْمَيِّتِ تَدْمَعُ عَيْنُهُ عِنْدَ الْمَوْتِ فَقَالَ ذَلِكَ عِنْدَ مُعَايَنَةِ رَسُولِ الله (صلّى اللهُ عَلَيْهِ وَآلِه) فَيَرَى مَا يَسُرُّهُ ثُمَّ قَالَ أَ مَا تَرَى الرَّجُلَ يَرَى مَا يَسُرُّهُ وَمَا يُحِبُّ فَتَدْمَعُ عَيْنُهُ لِذَلِكَ وَيَضْحَكُ 

Narrate through a chain of reliable narrators that Abu Abd-Allah Imam Sadiq (عليه السلام) said:

“Regarding a dying person his eyes shed tears at the time of death. Then the Imam said, “This happens when seeing the Messenger of Allah (صلى الله عليه وآله), so he sees that which makes him happy. Don’t you see that when a person sees that which makes him happy his eyes shed tears while he laughs.”

[Source: al-Kafi, Vol. 3, Pg. 133]

Hadith 6:

وعن محمد بن على عليه السلام قال : مرض رجل من أصحاب الرضا عليه السلام فعاده فقال : كيف نجدك؟ قال : لقيت الموت بعدك يريد به ما لقيه من شدة مرضه.

فقال : كيف لقيته؟ قال : شديدا أليما.

قال : ما لقيته انما ما يبدؤك به ويعرفك بعض حاله ، انما الناس رجلان مستريح بالموت ، ومستراح منه (به) ، فجدد الايمان بالله وبالولاية تكن مستريحا.

ففعل الرجل ذلك ثم قال : يا ابن رسول الله هذه ملائكة ربى بالتحيات والتحف يسلمون عليك وهم قيام بين يديك ، فأذن لهم بالجلوس.

فقال الرضا عليه السلام : اجلسوا ملائكة ربى.

ثم قال للمريض : سلهم امروا بالقيام بحضرتي؟ فقال المريض : سألتهم فزعموا انه لو حضرك كل من خلقه الله من ملائكته لقاموا لك ، ولم يسجدوا (يجلسوا) حتى تأذن لهم ، هكذا أمرهم الله عزوجل.

ثم غمض الرجل عينيه وقال : السلام عليك يا ابن رسول الله هكذا شخصك ماثل لى مع أشخاص محمد صلى الله عليه وآله ومن بعده من الائمة عليهم السلام وقضى الرجل

Narrated from Muhammad bin Ali Imam Taqi (عليه السلام) that,

A man from the companions of Imam al-Ridha (عليه السلام) fell ill so the Imam visited him and said to him, "How do you find yourself?"

He said, "I have met death after you - meaning what he had experienced from the severity of his illness."

Imam (عليه السلام) said, "How did you meet it"

He said, "Severely painful"

Imam (عليه السلام) said, "You did not meet it, in fact it is just the begining for you and makes you aware of some of its conditions.

There are two types of people – one who is at rest/ease through death and one from others are at ease through his death. So renew belief/faith in Allah and in divine authority (Wilayah) – you will be the one at rest (through death)."

So the man did so and then said, "O son of the Messenger of Allah (صلى الله عليه وآله), these are the angels of my Lord, with greetings and gifts, they greet You while they are standing before You. So give them permission to sit."

Imam (عليه السلام) said, "Sit down, O angels of My Lord"

Then the Imam said to the man, "Ask them if they were commanded to stand in my presence? 

He said, "I asked them, and they claimed that if all the angels whom Allah created were present with You, they would stand for You, and they would not sit until You give them permission. This is what Allah (عز وجل) has commanded them."

Then the man closed his eyes and said, "Salutation be upon You, O Son of the Messenger of Allah - You are presented to me along with Muhammad (صلى الله عليه وآله), and the Imams (عليهم السلام) after Him." 

And the man died.

[Source: al-Dawaat, by Qutb al-Deen Rawandi, Pg. 248]