There is no remissness in sleep, it is only when one is awake that there is remissness when you delay saying the prayer till the time for the next prayer comes.
The Messenger of Allah (ﷺ) was on his journey. They (the people) slept abandoning the Fajr prayer. They awoke by the heat of the sun. Then they travelled a little until the sun rose high. He (the Prophet) commanded the mu'adhdhin (one who called for prayer) to call for prayer. He then offered two rak'ahs of prayer (sunnah prayer) before the (obligatory) fajr prayer. Then he (the mu'adhdhin) announced for saying the prayer in congregation (i.e. he uttered iqamah). Then he led them in the morning prayer.
We were in the company of the Messenger of Allah (ﷺ) during one of his journeys. He overslept abandoning the morning prayer until the sun had arisen. The Messenger of Allah (ﷺ) awoke and said: Go away from this place. He then commanded Bilal to call for prayer. He called for prayer. They (the people) performed ablution and offered two rak'ahs of the morning prayer (sunnah prayer). He then commanded Bilal (to utter the iqamah, i.e. to summon the people to attend the prayer). He announced the prayer (i.e. uttered the iqamah) and he led them in the morning prayer.
حَدَّثَنَا مُحَمَّدُ بْنُ الْمُثَنَّى، حَدَّثَنَا مُحَمَّدُ بْنُ جَعْفَرٍ، حَدَّثَنَا شُعْبَةُ، عَنْ جَامِعِ بْنِ شَدَّادٍ، سَمِعْتُ عَبْدَ الرَّحْمَنِ بْنَ أَبِي عَلْقَمَةَ، سَمِعْتُ عَبْدَ اللَّهِ بْنَ مَسْعُودٍ، قَالَ أَقْبَلْنَا مَعَ رَسُولِ اللَّهِ صلى الله عليه وسلم زَمَنَ الْحُدَيْبِيَةِ فَقَالَ رَسُولُ اللَّهِ صلى الله عليه وسلم " مَنْ يَكْلَؤُنَا " . فَقَالَ بِلاَلٌ أَنَا . فَنَامُوا حَتَّى طَلَعَتِ الشَّمْسُ فَاسْتَيْقَظَ النَّبِيُّ صلى الله عليه وسلم فَقَالَ " افْعَلُوا كَمَا كُنْتُمْ تَفْعَلُونَ " . قَالَ فَفَعَلْنَا . قَالَ " فَكَذَلِكَ فَافْعَلُوا لِمَنْ نَامَ أَوْ نَسِيَ " .
We proceeded with the Messenger of Allah (ﷺ) on the occasion of al-Hudaybiyyah. The Messenger of Allah (ﷺ) said: Who will keep watch for us? Bilal said: I (shall do). The overslept till the sun arose. The Prophet (ﷺ) awoke and said: Do as you used to do (i.e. offer prayer as usual). Then we did accordingly. He said: Anyone who oversleeps or forgets (prayer) should do similarly.