I've seen somewhere (patch notes?) that the player is made invulnerable after "totally losing control" in a Singularity, but it doesn't feel like it's enough.
There are moments when even though the player might still be able to break free, they are effectively not able to maneuver. I'd say this happens any time the player is fully within the black circle boundary of a Singularity. Right now (~0.27) enemy projectiles, "burn orbs", Champ Celestial explosions, and collisions from wide enemies like Juggernauts and Eclipses can still hit an almost-but-not-100%-helpless player.
A salty example situation: https://media.discordapp.net/attachments/335955442129698816/671990914490564608/Replay-2020-01-29-0004-32.mp4