What happens if Hawk Eye determines a call was wrong, but no player challenged the call?

They're not using lines judges at the 2021 Australian Open this year due to the pandemic, an effort to reduce the number of people involved in the matches and the tournament in general. We saw the same thing in some tournaments late last year post Covid. All line calls are done by Hawk Eye in real time, on all courts of the tournament. Like usual when the ball is close to the line, it's shown on the screens for the players and observers to see as if there was a challenge in previous years.

Hawk Eye calls all out balls as soon as they happen even making the "out" sound you hear (it's Hawk Eye, not the umpire). So the are no player challenges in 2021 Australian Open. Hence you saw a player getting a point without making a challenge and the replay was shown.

In tournaments that Hawk Eye is not used to make calls automatically, when an improper call is made, without making a challenge, the point remains as called by the chair umpire or the lines judges. In these tournaments, players aren't shown Hawk Eye replays without a challenge.

Replacement of the lines judges by automatic electronic calls is likely to become the new norm in the near future. With the presence of Hawk eye, and also specially after Novak Djokovic hit a lines judge at 2020 US Open, it's likely we've seen the last of lines judges at the grand slams tournaments. Use of Hawk Eye comes with an extra cost where it can't be afforded at all tournaments. So we'll be seeing the lines judges at smaller events for a long time.