Al-Sha'bi (may Allah have mercy on him) narrates that a man named Ayyub bin Bariqah snatched a piece of jewellery from a man, and the case was brought before Sayyiduna Ammar bin Yasir (may Allah be pleased with him). Sayyiduna Ammar (may Allah be pleased with him) wrote to Sayyiduna Umar bin al-Khattab (may Allah be pleased with him) about it, and he wrote back: Whoever robs in broad daylight, give him an exemplary punishment, then let him go and do not cut off his hand.
In another narration, a man who had snatched a piece of jewellery from a slave girl was brought to Umar bin Abd al-Aziz (may Allah have mercy on him), and Umar bin Abd al-Aziz (may Allah have mercy on him) did not cut off his hand. He said: He snatched this in broad daylight.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب السرقة / 17293