Turn on Replay in Settings, System, and the overlay keeps the last minutes of your calls in your browser's memory. When something happens worth keeping, press the Replay mark on the video, or Alt+Shift+R, and the replay is saved to your downloads as a video file. Save this call keeps only the conversation you are in.
Choose how far back it reaches (up to 15 minutes), whether the clip shows the stranger alone, side by side with you, stacked upright for phones, or with you in a corner, and whether it has the sound of both of you, only the stranger, or none. Your side is what the stranger saw and heard, so camera and voice effects stay on. Nothing is uploaded, and turning Replay off or closing the tab forgets it.
Replay never keeps a stranger the explicit camera check flags: everything recorded of them is dropped. Recording people without their permission is against the law in some places, so only save and share clips you are allowed to.