According to our current understanding of physics, as an object with mass approaches the speed of light, its relative time dilation increases. This means that time appears to pass more slowly for the moving object compared to a stationary observer.
However, it is important to note that according to the theory of relativity, it is impossible for an object with mass to reach or exceed the speed of light in a vacuum. The theory of relativity predicts that as an object with mass approaches the speed of light, its relativistic mass and energy increase, requiring an infinite amount of energy to reach the speed of light. This is often referred to as the "mass-energy equivalence" principle, famously summarized by Einstein's equation, E = mc².
So, in practice, it is not possible for an object with mass, including humans, to travel at the speed of light. Therefore, the scenario you describe, where time stops and aging halts, does not occur for objects with mass.
However, for massless particles like photons (particles of light), they always travel at the speed of light and do not experience time in the same way as objects with mass. From their perspective, there is no passage of time.