Upvote:5
It doesn't matter when your visa expires. If your program has ended, you cannot enter the US in F-1 status. The immigration officer at the border will check your I-20 to ensure that you are eligible for F-1 status; if your program has ended, you won't have a valid I-20.
To enter the US, therefore, you'll need a B visa unless you're eligible for the visa waiver program or other visa-free entry.