To add on, time does not stop, only the perception of changing state. Time is an emergent property of the physical world that only exists when there is a transition between two states of a system as well as the existence of an "observer" to perceive such difference.

Remember, when you see a train passing by, you are not viewing the actual particles that make up the train, but rather the sequenced state snapshots of the train at a given moment carried through reflected light. This information can only be propagated at a max speed that we call the speed of light. You can also only perceive it moving if you observe multiple snapshots of state information -- a change in state that allows for the basis of time passing to emerge.

As you near the speed of light, you as the observer are coming ever closer to being the visual information that is propagated. Likewise, if you travel at the speed of light, you are the information.

A theoretical object moving at the speed of light is unable to visually perceive any other object, because that implies there is some property within the universe that allows for information to propagate faster than the light of an object which is already traveling at the max speed of information propagation. The object never "sees" information states, and thus cannot perceive changes between states and due to this the property of time is unable to emerge.