It is like 50% of chance to reproduce and it seems it is occurring only 1 time per character spawn as it has never occurred twice on same character.
Die by being shot by someone or get eaten by zeds.
Instead of "Respawn" press "Exit" to go to the lobby.
Choose from the list of characters the one you created and played with
Press "Play" and join the last server played.
You will notice that your killed character is alive and put back in time 2 minutes.