way back in the old days, there was a dauber in that position.
you would fill the cavity with read lead.
the red lead was used for lubrication purposes when working between centers.
you take a small dab of red lead and insert it into the center-drilled work ends, then place it between dead centers.
since we don't use many dead centers , the practice is fallen from favor
lead is carcinogenic, that too has been a reason for its demise