A Junub can stay at home without taking a bath but with ablution Sahih al-Bukhari 286
Arabic hadith text
حَدَّثَنَا أَبُو نُعَيْمٍ، قَالَ حَدَّثَنَا هِشَامٌ، وَشَيْبَانُ، عَنْ يَحْيَى، عَنْ أَبِي سَلَمَةَ، قَالَ سَأَلْتُ عَائِشَةَ أَكَانَ النَّبِيُّ صلى الله عليه وسلم يَرْقُدُ وَهْوَ جُنُبٌ قَالَتْنَعَمْ وَيَتَوَضَّأُ.
Translation
Narrated Abu Salama
I asked `Aisha "Did the Prophet (ﷺ) use to sleep while he was Junub?" She replied, "Yes, but he used to perform ablution (before going to bed).