Background checks
I don't want to reveal about 1 company I had worked for to my new employer, can I hide it? Will they figure it out in the background check?
You can hide, they will never know. Actually nobody cares!!
How does background check actually work? I mean if a company has shut down, for example, how would the next company know whom to call to check?
You will be asked to provide a contact of the founder, or HR perspn then, or a payslip, form 16, or atleast one colleague who worked there who can be contacted now to verify as proof,
Your PF account will always reveal the details, right?
If it was a full time position anytime in last 5 years reveal it. If you r joining a startup they may not care to do an exhaustive check - however If the new firm is an established one, they can ask for access to your 26AS (to verify you were not moonlighting in your prev jobs).