You have not specified what standard the vocalists possess, and that will vary greatly - some amateurs will have a wonderful sense of timing, some pros not so good - and vice versa.
So as it stands the question is regarding all opera and all musical singers. The orchestra (or band) may well be hidden down in the pit, not able to see the singer well at all - and mostly will be reading the dots, sometimes for the first time. They will be aware that the conductor knows his job best - conducting, so will be relying on the conductor for timing and cues. Why not? The singer will be doing the job they know best - singing, and may well be blissfully unaware of timing issues.
So, the safest is for the players to follow the conductor, who will follow, and sometimes prompt, the singer. In opera, musicals (and just about any other vocal lead music), the singer always has precedence. If they go wrong, everything will sound wrong, and it's up to the players to make them sound 'right'. If that means speeding up, slowing down, missing a beat, whatever, that's what needs to happen.
You cannot stop in the middle of a performance and tell the singer they're speeding up/slowing down. After, maybe. But in the moment, the band plays on, as we say.
So, singer sings blissfully away, conductor watches them, conducts, and everyone stays together. Is there a better way?
P.S. if there's only a piano for accompaniment, things are so much easier. Harry Connick Jr (I think), has a fabulous you tube , where he gets the audience back in time during a number. Well worth a watch. Please, someone, find it for us.
Harry Connick Jr link provided by Laurence Payne: https://laughingsquid.com/how-harry-connick-jr-got-his-clapping-audience-back-on-beat-with-one-simple-note/#:~:text=While%20performing%20%E2%80%9CCome%20By%20Me,extra%20note%2C%20Connick%2C%20Jr