Can a batsman be run out after the ball is dead?

I don't think you can get run out after the umpire signals over. When the umpire signals over, the six deliveries are all finished, and there is no further play.

The meaning of the dead ball is no further actions can be performed after the ball is declared as dead. That means neither batsmen can run nor fielders can run-out them.

See Dead ball - Wikipedia

In cricket, a dead ball is a particular state of play in which the players may not perform any of the active aspects of the game. In other words, batsmen may not score runs and fielders may not attempt to get batsmen out.

Law 22.4 call of over states that

When 6 valid balls have been bowled and when the ball becomes dead, the umpire shall call Over before leaving the wicket.

and Law 23.3 states

Neither the call of Over, nor the call of Time is to be made until the ball is dead.

As umpire already signaled over that means ball is dead and he can't be run out.