In India.

it didn't

Buddhists never left India. At one point Buddhists were one of the majority religions in India; but Hindu priests became entrenched in India's politics and used their position to reinforce Hinduism. Between that and Buddhism's belief in no gods, lead to a decline in popularity there. In Modern times Buddhism is flourishing again. Many of the dailits (outcast caste) are becoming Buddhists.

Actually Buddhism had and still has a significant effect on India. At one time Buddhism was the largest religion in India. This lasted for quite some time until Hindu priests used their political power to dampen the spread of Buddhism and cause it to decline. Regardless of ancient history, the Buddha's teachings were brought into Hinduism and the Buddha is still revered by Hindus as the ninth avatar of Vishnu.

Buddhism originated in India, and it never caught on in India. Buddhism was then introduced in China, Korea, and Japan