Nope that is Boss's grave. Big Boss stop's snake from killing himself but the foxdie implanted in snake finally kills Big Boss. Big Boss being the bad ass he is fights off foxdie for a good 5 minutes as other people it kills instantly....he tells Snake to just live for the rest of his days since he has accelerated aging because snake is actually a clone of Big Boss and pretty much as old as him at that point.
FOXDIE was an engineered retrovirus developed by the DIA for the Pentagon. It was programmed to kill specific people by identifying the person's DNA and their nanomachines, causing cardiac arrest.