Star is open,still motor is working

A possibility is that where the blue phase is broken the leg to the star point has shorted to earth. Have you done an IR test on the motor? The O/L's should have picked up the imbalance.

Blue phase is not broken,three star wires are coming out.And accordingly to vendors design only, two phase are shorted.So how it is possible,please explain.

"...without any problem"

That probably should be "without any PERCEIVED problem. if one connection is open, you are single phasing and even though the motor may be turning, you don't have full power available from it.

Beats me how it starts

My guess; what you thought of first, even with a bad ground path, which provides just enough rotation to get it started moving, then the load is so light that the single phasing once it is already moving provides enough power to keep it moving.

How do you know the B phase open?

6 wires are coming out,it is installed in a panel.and connected in a above mention way.

I have seen the thing like this also - it is possible with small motors. Power, I believe, is then reckoned not by multiplying by sq root 3 but by sq root 2.

But things are going... in not the way we know. Why?

Line voltage differs from phase voltage. The former produces different emf's in both remaining windings of the motor (that is, maybe better to say, the source, a generator , or a transformer produces) while the latter creates the same emf in the both.

Are you using Star-Delta starting perhaps? If so, then it could be that when you start it, there is a partial path but when running you end up losing one set of windings, but it is already spinning at that point, in which case refer to the above.

You really are not being very clear about what you have and what is being used to start it etc. Any chance you have a drawing you can post?