Jesus didn't cease to exist after his physical death on the cross. This is explained when He 'gave up the ghost.'Luke 23:46 "And when Jesus had cried with a loud voice, he said, Father, into thy hands I commend my spirit: and having said thus, he gave up the ghost."Not only did Jesus not cease to exist when He died, neither do we. We are made in His image. Physical death separates the soul from the flesh.
If the God-head could cease to exist then Jesus could not have raised from the dead. Rom 8:11 But if the Spirit of him that raised up Jesus from the dead dwell in you, he that raised up Christ from the dead shall also quicken your mortal bodies by his Spirit that dwelleth in you. If the Spirit was dead then how would a dead spirit raise a dead man?