We've known for a long time that Google Hangouts was meant to shut down, but most of us couldn't predict individual features would be slowly picked from their not-quite-dead body. That seems to be the case with the location sharing function that was previously found in Hangouts. As of v32, the convenient messaging feature was quietly removed.
Place sharing was added back in late 2013 and has been largely unchanged since its launch — aside, of course, from a few minor changes. Using it was as easy as pressing the place pointer icon and selecting a location using a draggable map overlay, or using your current location. Once the position has been sent, the receiver will tap it to show the destination and get directions.
There is no denying the usefulness of a feature like this, but it's hard to predict how much it was actually used. There may be plausible explanations for removing a feature that otherwise worked fine; for example, a Maps API may have been deprecated and updating to keep things working in Hangouts isn't worth the effort. There are already updates planned for the Places API, but it's not clear whether it will affect Hangouts. Nevertheless, the new update basically looks the same, minus a click to activate a share.
This is still Android, of course, so alternatives do exist. If you don't mind a more manual approach, simply open Google Maps, select a location and use the Share button to transfer it to Hangouts. Or you can just give in and do what Google obviously wants and switch to the Messages app, which, although buried slightly deeper in the UI, happens to have an almost identical feature.
The Hangouts shutdown was originally scheduled for the end of 2019 but was pushed back to June 2020, but there's no word if that schedule will be maintained. We're closing in on that point in the year, and with an update of any kind being released, it's safe to say that Google hasn't forgotten about this one.