He was helped by Sans. Gaster died in his machine, scattering him through time and space. Sans, who probably did a Genocide Run too, understood that this was a bad idea. He decided to stay in his Genocide Run and to be nice and friendly to stop this madness.

How did Gaster die?

Gaster most likely injected himself with high amounts of DETERMINATION, hallucinations are a common side effect of this- he states that shadows grow everywhere he goes, witch most likely caused him to trip and fall into the core.

Is Sans related to Gaster?

There are hints in game that Sans is somehow related to Gaster (his knowledge of the timelines, his secret lab, his genocide route attack is called Gaster blaster, etc.). But, as for what that relationship exactly is, nothing was cannonically confirmed. Sans speaks in Comic Sans.