You should either extend your visa or leave BEFORE it expires. The Chinese government does NOT take kindly to over extensions, even as little as a couple of hours, in the best of circumstances. Now, with the 100 day crackdown, would be the worst time to have an expired visa.

Get the extension or leave early.

DONT THINK YOU WILL BE ABLE TO COME BACK FOR A LONG TIME

You definitively will.  If you depart China from an airport within China, when you try to exit and pass IMMIGRATION you will be detained and not allow to proceed.  Will be interviewed by a few officials, forms filled out, a fine requested and paid by you in Rmb, and all of that will take time, maybe 3 or 4 hours, and I am sure you will miss your flight back home.  So, if you manage to get another flight, maybe kept at airport, or taken to a local jail for deportation procedures.  Maybe if you do act nicely, show lots of remorse, fake the fact that you did not know visa expired, ask forgiveness each three words, you will be given just a fine and deported.

Why risk that for 3 more days, and not a chance of getting another visa to enter China in years ?.  You can either go now to PSB and ask for a few days extension on the stay of your visa, to be allowed to exit legally, or go out of China on the date of expiration and do stay outside until you can catch a plane home.  If your flight leaves from HKG, go there and stay until your flight leaves.

Since you are not clear on your question, I am forced to a general answer.  What do you mean by "your visa expires 3 days before my flight home"?.  Is the period of time the visa is valid, or is the number of days you can stay ?

Ask for the extension!!!! 

Just FYI the fine is 500CNY per day. 

Go to the PSB, show them your flight ticket and ask for the 10 day exit stamp

Sometimes I don't get it. The first time I left china to go to work in the US my visa was expired by a couple of days, they didn't care at all and I went from Beijing to Kunming and from there out of the country. Even had a 24 hour lay-over in Kunming.

And I still got a visa and I am back in china.

Word is, that they are most likely to just kiss you good bye if your visa is overstayed for less than 10 days.  

The more days are on the clock, the less likely you are to ever get into the country again.

Having said this, you could be fined, put in detention, blacklisted for life, etc.

Why don't you just go to the PSB, smile and explain your situation? 

Well, lately they are cracking down.  However, normally, the officers have a little bit of decision making authority, just like at most consulates.  That is why you hear of mixed stories.  Some people are let through without a hassle and others get stopped.  They have protocols to follow, but some of it is up to them.  Notify your local police station and they will sort it out.  

You're not going to jail, but you are going to have a massive hassle and likely won't be allowed back for a few years. 

The immigration officer will command you to pay the penalty-500 yuan per day, so totally you need to pay 1500 yuan. Get prepared the money.

you should get an extention now so it wont expire

you should get an extention now so it wont expire

it can all depend on what officer looks at the paper work,  what mood they are in, what instructions they were getting,  even what nation you are from.

manybe nothing happens and you just leave.

But as noted, they can fine you 500 yuan a day, even detain you in jail.  or detain you at airport and you miss the flight.

The local PSB can extend it very easily

go to beijing with your air ticket