This is accomplished by simply preserving
the player's body after disconnecting.

Bodies will despawn after the number of minutes
specified by the "rejointimeout" console variable (float).
A value of 0 disables the feature completely.

Clients rejoining are identified by their IP address,
and may rejoin even if the server is full or joins are disabled,
for as long as their body remains.

From a technical standpoint, when the user disconnects,
the player they were controlling does not leave,
the underlying player_t just keeps working normally,
except it does not receive any input anymore.
When the user reconnects, they are simply "relinked"
to their player_t.

Those "soulless" players can be identified through
their "quittime" field, which is the number of tics
elapsed since the user disconnected, or zero
if still connected. "quittime" is exposed to Lua.