Stasis

The stasis is a biological technology created by the Homelanders rougly at the same time as the creation of a steady dummies' production line.

Early hypotheses
Since the dawn of sapience, the Homelanders suspected that their existence was finite. To verify or deny this statement they observed animals with shorter hypothetical life cycles. After some time their hypothesis was fully confirmed.

To prevent loss of minds, they worked hard on a possible solution, biological or not. Certain experiments with dummies showed that exposing a living organism to sub-zero temperatures led to a peculiar conservation of this organism. All body functions slowed down dramatically, but didn't stop competely. It led to a hypothesis that brains could be frozen in a similar way, until the time when new technologies of life prolongation would be created.

This hypothesis was disproven when studies showed that the damage caused to highly-organised living organisms by cryoconservation was irreversible.

Suspended animation
After the failure with cryonics, the Homelanders turned to nature. Certain animals were hibernating during cold periods, which proved of interest to the researchers. Various test and studies, along with steady improvement of cryotech resulted in optimistic data about possible brain stasis.

After several decades of  experiments,  studies and countless lost dummies, the Homelanders finally found a way to preserve brains for several SCs (stellar cycles) without severely damaging them. A rare genetic mutation, along with chemical- or cryo- induced suspended animation had bought some time for those whose time was running out.

It wasn't a panacea of course, but with additional time for technological development the Homelanders were able to preserve each and every one of their number without losing anyone.

When the intelligence-uploading technology was created and properly tested, the preserved minds were uploaded to the first servers.