Can I immigrate to a country where I don't have to support my parents at home?

It depends on which country you immigrate to. If you immigrate to Singapore or South Korea, you still have to support the elderly, because children in Singapore and South Korea also have the obligation to support the elderly. If you immigrate to the United States, Britain, Japan or other western countries, you don't have to support them, because the laws of those countries have no obligation for children to support the elderly, and there is even no concept of raising children to prevent old age.