Can Guangzhou social security stop paying for three years and transfer to Foshan to continue paying?

You can apply for social security and transfer to Foshan

Print the payment voucher with your ID card and social security card at the social security center in Guangzhou, and then hand it over to the social security center in Foshan for the transfer of social security payment relationship.

Guangdong's old-age insurance is co-ordinated by the whole province, and the insured with Guangdong household registration can re-pay the insurance premium in any city in the province without handling social security transfer.

Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.