Is it possible to enter someone's Facebook account, without knowing or changing the password?

[Inquiring]

1. Make sure you didn't actually stay logged in on someone else's device.

2. Make sure that if you click "save password" on your computer/laptop that nobody has access to it. When you save your password there is a record within the browser. For example in firefox go to "firefox (top left) > options > security > saved passwords > view passwords." If you do this you can see all your saved passwords. Someone could have done this process on your computer when you were not around.

3. Make sure you use a secure network. Network protocol analyzers like wireshark can intercept the packets of data being sent to and from your computer. If you log into facebook when someone is running wireshark AND on the same network as you, they intercept your positive log in cookie from your browser. They can just throw this into a cookie manager and gain access to your account without changing the password. Bottom line: although they have to be pretty smart, dont risk being on the same network as someone you don't like/know unless you have to.

4. Try logging in with your credentials on your computer. If you use an app within a mobile device or tablet you may be decieved. The password to your account very well could have been changed without your knowledge. when a mobile application logs into something like facebook, twitter, netflix etc. it only uses your credentials the first time. Every other time you "auto logon" within the app is isn't retesting your credentials, but merely retaining the positive log in status that you originally had. Essentially someone could change your facebook password and you could still access it just like normal from an iphone but not from your computer.

I hope that made sense to you, that is really the only way I see your situation being possible. If it is not one of the solutions I listed then there is probably a very experienced and dangerous hacker on the loose. Good luck!