Info

Passwords are generally only stored on the device, unless shared across devices.

To get your eMail password you may need to go to the eMail provider's website,

(eg: Yahoo, Gmail etc.) and reset the "forgotten" password there so you can access your eMail.

You can likely do a similar reset "password" with other kinds of passwords / accounts etc.

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Re: Lost phone:

You might want to follow the tips in this link:

If your iPhone, iPad, or iPod touch is lost or stolen - Apple Support

PS: If you have back-ups of your iPhone data (eg on computer, iCloud, or external drive) it may be possible to transfer everything to another iPhone. If you have saved passwords in the back-up, you might be able to recover them that way.