Shri Rama killed Vali, when the latter was fighting with Sugriva.
No extra power was attached to the golden pendant being received from Indra and worn by Vali. The narrative that Vali receiving the power to take half the strength of his opponent might have emanated from folklore.
Vali, who was at his death-bed, asks Sugriva to become the King of Vanaras, to take care of his son Angada and to take the golden pendant before his death and wear it.
इमां च मालामाधत्स्व दिव्यां सुग्रीव काञ्चनीम्।
उदारा श्रीस्थिता ह्यास्यां सम्प्रजह्यान्मृते मयि4.22.16।।
'O Sugriva put on this divine golden necklace. It has great brilliance. Its present lustre may be gone when I am dead.'
तद्वालिवचनाच्छान्तः कुर्वन्युक्तमतन्द्रितः।
जग्राह सोऽभ्यनुज्ञातो मालां तां चैव काञ्चनीम्4.22.18।।
On hearing Vali's words, Sugriva became composed with no illfeeling. Considering it to be proper, he received with his permission the golden necklace.
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Sugriva fights with Ravana on arrival in Lanka.
When the one-to-one combat was physical, both were matched. However, when Ravana resorted to using sorcery, Sugriva jumps back to the place where Shri Rama stood.
बाहुत्तमैर्वारणवारणाभै |
र्निवारयन्तौ परवारणाभौ|
चिरेण कालेन भृशं प्रयुद्धौ |
संचेरतुर्मण्डलमार्गमाशु || ६-४०-२१Like unto great tuskers with their enormous arms resembling the trunks, those two warriors were keeping back each other, fought vehemently for a long time and moved speedily in a circular arena.
एतस्मिन्नन्तरे रक्षो मायाबलमथात्मनः |
आरब्दुमुपसम् पेदे ज्ञात्वा तम् वानराधिपः || ६-४०-२७
उत्पपात तदाकाशं जितकाशी जितक्लमः |
रावणः स्थित एवात्र हरिराजेन वञ्चितः || ६-४०-२८Meanwhile, Ravana decided to common using his magic power. Knowing it, Sugreeva flew into the sky triumphantly shaking off all fatigue, while Ravana, baffled by Sugreeva stood confounded there alone.
—-
So, neither the pendant contains any extra power nor Sugriva was defeated by Ravana here.
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However, during the war, Ravana’s missile made Sugriva unconscious.
स तम् गृहीत्वा अनिल तुल्य वेगम् |
सविस्फुलिन्ग ज्वलन प्रकाशम् |
बाणम् महा इन्द्र अशनि तुल्य वेगम् |
चिक्षेप सुग्रीव वधाय रुष्टह् || ६-५९-३९The enraged Ravana, taking that arrow with the speed of a thunder bolt of Indra the Lord of celestials and possessing the brilliance of a fire, hurled it to kill Sugreeva.
स सायको रावण बाहु मुक्तह् |
शक्र अशनि प्रख्य वपुह् शित अग्रह् |
सुग्रीवम् आसाद्य बिभेद वेगाद् |
गुह ईरिता क्रौचम् इव उग्र शक्तिह् || ६-५९-४०That arrow released by Ravana's arm reached Sugreeva, having a bodily splendour equal to that of Indra's thunder bolt, and pierced his body in its flight as formerly Guha's spear when he discharged it at the Krauncha Mountain.
स सायक आर्तो विपरीत चेताह् |
कूजन् पृथिव्याम् निपपात वीरह् |
तम् प्रेक्ष्य भूमौ पतितम् विसम्ज्मम् |
नेदुह् प्रहृष्टा युधि यातु धानाह् || ६-५९-४१Wounded by that arrow, which bereft him of consciousness, that warrior fell moaning to the earth. Beholding him falling on the ground, deprived of his senses in the battle-field, the demons raised a shout of triumph.
