CONFIG_SYS_SUPPORTS_KGDB is not available for thedefaultarchitecture x86.
Result is shown for architecture mips

CONFIG_SYS_SUPPORTS_KGDB (not configurable)

configname: CONFIG_SYS_SUPPORTS_KGDB

Linux Kernel Configuration
└─>Kernel hacking
└─>SYS_SUPPORTS_KGDB
In linux kernel since version 2.6.21 (release Date: 2007-04-25)