The optical observations of Ic-4 supernova (SN) 2016coi/ASASSN-16fp, from similar to 2 to similar to 450 d after explosion, are presented along with analysis of its physical properties. The SN shows the broad lines associated with SNe Ic-3/4 but with a key difference. The early spectra display a strong absorption feature at similar to 5400 angstrom which is not seen in other SNe Ic-3/4 at this epoch. This feature has been attributed to He I in the literature. Spectral modelling of the SN in the early photospheric phase suggests the presence of residual He in a C/O dominated shell. However, the behaviour of the He I lines is unusual when compared with He-rich SNe, showing relatively low velocities and weakening rather than strengthening over time. The SN is found to rise to peak similar to 16 d after core-collapse reaching a bolometric luminosity of L-p similar to 3 x 10(42) erg s(-1). Spectral models, including the nebular epoch, show that the SN ejected 2.5-4M(circle dot) of material, with similar to 1.5M(circle dot) below 5000 km s(-1), and with a kinetic energy of (4.5-7) x 10(51) erg. The explosion synthesized similar to 0.14M(circle dot) of Ni-56. There are significant uncertainties in E(B - V)(host) and the distance, however, which will affect L-p and M-Ni. SN 2016coi exploded in a host similar to the Large Magellanic Cloud (LMC) and away from star-forming regions. The properties of the SN and the host-galaxy suggest that the progenitor had M-ZAMS of 23-28M(circle dot) and was stripped almost entirely down to its C/O core at explosion.