What if we could stop time and remain conscious ?

The brain has a special class of cells called pacers cells. The pacers cells are a group of neurons that fire at a fixed rate. They as act as a metronome for the brain, much in the same say as a metronome does for a musician. A metronome ticks at a fixed tempo, and is used by a musician as the standard by which they process all the timing in the music; quarter, half, whole notes, pauses, etc. 

Our human concept of time is based on how the brain relates changes of state, which enter the brain through our sensory systems, to the pacers cells. For example, it is no coincidence that our basic unit of time; second, is at the pace of the human heart; at rest. The brain feeds the heart, pulses of energy, which are timed to the pacer cells. We as humans might then project the second as a universal standard. 

That being said, your question amounts to what would happen to consciousness and our perception of time and reality, if we lost total function in the pacers cells; neural metronome stops. More than likely, the brain would reassign the role of the pacer cell hardware, with a software equivalent. In other words, the brain would try to use a nonphysical or software-based replacement. It may try to use a set of memories, which had been previously synchronized to the pacers cells. This becomes the new standard. An analogy is a symphony orchestra is playing. The metronome stops, but the music must go on. The members of the band will begin to use other members, such as a drummer, as the new pacer. The drummer, who was also using the metronome, may try to use the violins, etc. There will be some process control adjustment going on. 

Consciousness would depart from the collective human time projection since the pacer cells of the human brain are defined by human DNA. That person would step out of collective human time and walk to the beat of their drum which is not physical per se but is more based on ethereal information. This could explain spiritual projections, which are not physical, but soonheless, it will have similar consciousness properties not connected to earth time. For example, the wandering soul synchronizes time to a tragic event that repeats; metronome. I prefer the concept of time potential, instead of time, because it allows one to define the nature of time in a way that is not an unconscious projection of the pacer cells, and how brain unconscious relates all changes in what we call time. If you compare time to distance, distance can be measured with a passive device like a ruler. 

On the other hand, Time needs a dynamic device; clock, with the dynamics requiring energy. I am not aware that the brain has any potential energy pacer standards, which are planned as time potential. But it does have a time standard based on the projection of the pacer cells. The concept of time tends to keep physics more unconscious. 

I sort of personifying what happens when you do not use the pacer cell projection, though; I still have full function in my pacers cells. The result is I can see the collective human time, but I am not constrained to this by default. There is no rule in science about the calibration of the mind, to a universal standard instead of a projection standard. I try to do it anyway since it is good scientific practice. 

Time is a mental abstract, not a physical thing one can save in a bottle. Time potential is different.