I20 must be signed within six months before crossing the border. Usually you withdraw your signature, but they didn't renew it for you, did they?
If you have a signature within six months, you can come back (because the customs officers don't know that you are withdrawing it), but this is actually an illegal return, which means that if you want to renew or transfer to H 1B in the future, it will be very troublesome to find a green card. You'd better wait for re-entry before applying for a visa. If you want to go early, you can only get a tourist visa.
In addition, I want to remind you that your ticket information for leaving the United States is for OIE. If you don't give it to them within the time limit, your file will have a permanent bad record. I don't know if you have communicated with OIE. Theoretically, they should have told you that you can't be in the United States now. You should return to China within the time limit and then give them your ticket certificate.
By the way, the new semester has begun. If you dropped out of school last semester and are not registered now, the school has already told the Immigration Bureau about your dropping out. Now it is not a question of whether you can come back, but whether you can stay in the United States.
Theoretically, the United States will not repatriate overstayers, but you have expired (F 1 you don't need to register directly after expiration), and coming back is just a loophole. Note that it will be very, very difficult to apply for a new visa after being found out.
You are at least a college student. There is no need to use the status of illegal resident, which is very bad for you. I'm back. I can't change my work visa or green card. You can only be an illegal worker. You should continue to hang out in America, contact OIE people at school and see what to do. OIE people can modify it in your file.
If you drop out of school this semester, please contact OIE immediately, and remember that you must leave the United States within two weeks after dropping out of school (or see if OIE can give you an extension)