Officiant here. Definitely have had this happen. It is usually pretty awful, and confusing. And it is, in most situations, (except of course same-sex couples) the groom. I’ve only ever seen the bride skip out on tv.
The party usually waits 10-15 minutes after the designated start time. Then there’s an awkward moment, and usually someone gets a call or text, or is sent to deliver the bad news. This generally results in tears, and statements of, “I knew it!” Some folks shuffle the bride off, and then usually Dad or senior member of the family makes an awkward statement.
If there was a reception with a meal planned, folks are either invited to stay and eat or the food is sent to a shelter.
And that's really about it.