If a batted ball strikes a runner while he is still on hois starting base (in fair territory) is he out or is the base a safe spot?

The runner is not out.
If the closest fielder is behind the runner and the ball strikes the runner who is on base in fair territory it’s a dead ball. The batter is awarded a base hit and any runner on base is awarded the next base if forced.
If the closest fielder is in front of the base runner and the batted ball strikes that fielder and hits the runner it’s considered hitting the ground and a live ball.

I agree with stick... but it doesn't matter whether a batted ball strikes the fielder..

if the closest fielder is in front of the runner and it strikes a runner while on or off the base and no other fielder has a chance to make an out it is a live ball

Hey Guys
If a runner is ON the base and is hit by the ball, it is a live ball.. PERIOD
Coop3636

BJ, that’s correct. It can pass thru a fielder without contacting thatvfielder. passes thru a fielder? Good catch.
Coop3636. that’s not true if the closest fielder is behind the runner. If the runner is on the base it’s a dead ball and the batter is awarded a base hit. Any other runners are moved up one base if forced.

Whats the call if the ball is hit low and the runner jumps straight up to avoid getting hit and the ball hits him while he is in the air but he comes back down on the base ?

The base runner loses the protection and presumption of being "safe" ... Then the umpire is into the same analysis as before ... He "could" be either safe or out, but he's NOT presumed safe if not in contact with the base when struck ...

One more comment to BJ's post. Assuming there was a fielder "in front" of the runner and the ball goes by the fielder untouched and then hits the runner that is a live ball UNLESS, there is another fielder behind the runner who in the umpire's judgement could have made the play had the ball not hit the runner. It's an odd nuance but has happened.

Even if the runner is on the base when struck by the batted ball, if the runner is attempting to interfere with the batted ball the umpire can call the runner out.

Here is a good discussion of all the various situations: https://baseballrulesacademy.com/runner-is-hit-by-a-batted-ball-safe-or-out-it-depends/

The most interesting one is the "phantom fielder" interpretation in MLB.

If a baserunner is hit by a fair batted ball while standing on a base, the runner is out, unless the ball has already passed an infielder or the infield fly rule has been declared.

Spider9188, it depends where the closest fielder is.
If the closest fielder is behind the baserunner it’s a dead ball, batter is awarded a base hit and any baserunners move up a base if forced.
If the closest fielder is front of the baserunner then it’s a live ball.

spider9188 ... You are incorrect ... You have accurately stated the Major League Baseball rule ... But the Senior Softball rule is as just about everyone except you has stated ...

Thanks all. I now understand the rule.