is it possible that the grafts are not safe or (came out) after one month?

If the grafts were not handled properly during surgery, the implanted grafts will not take and your body will reject it.  If your surgery was a success, it would be very difficult to dislodge a graft after one month.

Actually, it is quite normal to experience the shedding of
hair shafts after a hair transplant procedure. The formation of scabs occurs as
the skin heals underneath the crusting. Therefore, it is not likely that the follicles
themselves have slipped out. It takes nine days for enough healing to occur so that the follicles are permanently embedded beneath the skin.Yet, many patients feel concerned that the grafts
are coming undone. But actually, the shedding is a good sign. It indicates that new hairs are being produced. And the shedding of old hairs
occurs simply to make way for the new sproutings.

The hair shafts that
were transplanted during your procedure will continue to fall out for a few
months. But again, don’t feel anxious or worried since this is a natural part
of hair growth after your surgery.

Usually around month four, the signs of new hair will become
more prominent. 

After 1 month it would be very difficult to remove the follicle.  The hair falling out with a scab is a normal part of the process.  The toughest part is the waiting until the hair starts to grow which is from 4-8 months post procedure.  Good luck