Rule 1: 1. The participle of manner: قَائِلًا
An active participle in the indefinite accusative tells how or in what state the subject did the action: دَخَلَ قَائِلًا he entered saying, رَجَعَتْ بَاكِيَةً she came back weeping. It agrees with the person it describes in gender and number, and it is always indefinite, however definite the subject. Grammarians call it اَلْحَالُ, the state. قَائِلًا (feminine قَائِلَةً, plural قَائِلِينَ), the participle of قَالَ, is the commonest of all, introducing direct speech after verbs of motion or greeting.
دَخَلَ الْمُعَلِّمُ الصَّفَّ قَائِلًا: اَلسَّلَامُ عَلَيْكُمْ.
dakhala l-muʿallimu ṣ-ṣaffa qāʾilan: as-salāmu ʿalaykum
The teacher entered the class saying: peace be upon you.
صَافَحَ الْجِيرَانُ الْحَاجَّ قَائِلِينَ: حَجًّا مَبْرُورًا!
ṣāfaḥa l-jīrānu l-ḥājja qāʾilīna: ḥajjan mabrūran
The neighbours shook the pilgrim's hand, saying: an accepted Hajj!
Accusative sound plural ـِينَ, agreeing with الْجِيرَانُ.
رَجَعَتِ الْأُمُّ مِنَ الْمَطَارِ بَاكِيَةً.
rajaʿati l-ummu mina l-maṭāri bākiyatan
The mother came back from the airport weeping.
خَرَجَ الْحُجَّاجُ مِنْ مَكَّةَ فَرِحِينَ.
kharaja l-ḥujjāju min makkata fariḥīna
The pilgrims left Mecca rejoicing.
An ordinary adjective can stand in the same accusative of state.