A recently-discovered class of outflows, extremely high-velocity outflows (EHVOs), may be key to understanding feedback processes as it is likely the most powerful in terms of mass-energy. These EHVOs have been observed at redshifts 1.052 < z em < 7.641, but the potential connection with outflows in emission had not been studied. We find that EHVOs, albeit their small numbers at the moment, appear to show distinct C iv and Heii properties. In particular, EHVOs are more predominant in quasars with large blueshifts of the C iv emission line, suggesting a connection between emission and absorption outflowing signatures for these extreme outflows. We also find incipient trends with the maximum velocity of the outflows, which is similar to what has been previously found in BALQSOs, but now extending previous studies to speeds up to ∼0.2c. We find the bolometric luminosities, Eddington ratios, and black hole masses of our sample are overall very similar from the general quasar population upon considering their C iv emission properties. This is close to the case for Heii EW as we observe a tentative upper limit to the He ii strength for a quasar to host an EHVO. This study shows that extreme outflows such as EHVOs appear in quasars that are clearly a distinct class from the overall BALQSO population, and solidify the relation between outflows observed in emission and in absorption.