For a hypothetical situation, imagine a program that saves its user's password, then automatically signs them in without prompting them for their password again. The password must be secured somehow, but if it were to be encrypted, wouldn't there then be an unencrypted password or key somewhere?

I know many programs that do this, but as I've been researching I've found no reliable ways to protect this data. Computer security is usually taken very seriously, with mathematically proven algorithms for most encryptions, ssl, etc. But with this, most of the advice I've found is to hide it somewhere in the computer, or to try to split it up or otherwise make it "difficult" to find. That doesn't sound like very secure advise.

Is there any way for a program to securely store a password, without anything left in plaintext, and without requiring a user to input a password? I'm sorry if this question is too open ended, but I would appreciate it if someone could at least point me in the right direction.