Broad-line type Ic Supernovae ( BL-Ic SNe ) are characterized by high ejecta velocity ( \gtrsim 10 ^ { 4 } km s ^ { -1 } ) and are sometimes associated with the relativistic jets typical of long duration ( \gtrsim 2 s ) Gamma-Ray Bursts ( L-GRBs ) . The reason why a small fraction of BL-Ic SNe harbor relativistic jets is not known . Here we present deep X-ray and radio observations of the BL-Ic SN 2014ad extending from 13 to 930 days post explosion . SN 2014ad was not detected at either frequency and has no observational evidence of a GRB counterpart . The proximity of SN 2014ad ( d \sim 26 Mpc ) enables very deep constraints on the progenitor mass-loss rate \dot { M } and on the total energy of the fast ejecta E . We consider two synchrotron emission scenarios for a wind-like circumstellar medium ( CSM ) : ( i ) uncollimated non-relativistic ejecta , and ( ii ) off-axis relativistic jet . Within the first scenario our observations are consistent with GRB-less BL-Ic SNe characterized by a modest energy budget of their fast ejecta ( E \lesssim 10 ^ { 45 } erg ) , like SNe 2002ap and 2010ay . For jetted explosions , we can not rule out a GRB with E \lesssim 10 ^ { 51 } erg ( beam-corrected ) with a narrow opening angle ( \theta _ { j } \sim 5 ^ { \circ } ) observed moderately off-axis ( \theta _ { obs } \gtrsim 30 ^ { \circ } ) and expanding in a very low CSM density ( \dot { M } \lesssim 10 ^ { -6 } M _ { \odot } yr ^ { -1 } ) . Our study shows that off-axis low-energy jets expanding in a low-density medium can not be ruled out even in the most nearby BL-Ic SNe with extensive deep observations , and might be a common feature of BL-Ic SNe .