Death rates increase every year due to naturally occurring mechanisms in the body. Consider those mechanisms as a function with the body as a parameter and the output as a more aged body (or rather a body with higher probability of failure).
If the body reaches a point where the death rate ceases to increase year per year, it would suggest that those same naturally occuring mechanisms, thought of as a function, approaches some asymptote.
Note this doesn't necessarily mean you stop aging (in appearance), just that your body's rate of failure no longer increases. This suggests that if the reasons for failure can be treated properly, perhaps the body can remain in that equilibrium state indefinitely.
This study provides some preliminary evidence that such an asymptote may exist in the body's natural mechanisms. Both controversial and exciting. Worth exploring further.