Debug processes that crash at random while being created on Linux hosts

Workloads run on a cluster of Linux servers, and some of their processes crash at random while they are being created. The interviewer has one hidden cause in mind and acts as the system: you say what you would check or which command you would run, and they tell you what you see. Narrow it down step by step to the cause, explain your reasoning at each step, and say how you would fix it and keep it from coming back.