file: /proc/sys/net/ipv4/conf/interface/promote_secondaries
variable: net.ipv4.conf.interface.promote_secondaries
Official reference

When a primary IP address is removed from this interface promote a corresponding secondary IP address instead of removing all the corresponding secondary IP addresses.

Nb: per interface setting (where “interface” is the name of your network interface); “all” is a special interface: changes the settings for all interfaces.