I think is up to each case, city & when it happens.

I think every year government gets tighter or at least thats what I've heard.

I know someone who last year had a similar case to yours and entry & exit dept was quite concious about it and they gave the visa in advance coz the passport was about to expire. I think the main issue is always visa so you should've worried first about visa than passport. If you are already started a procedure you better go personally to entry & exit dept and expose your case to get a real solution. I dont think you will get much real help here since as I said each case is different and maybe they use criteria for each one.

I knew someone who overstayed almost 6 months with an expired visa. Sounds incredible but I knew the guy and I know is true coz I saw it.
He used to worry about his visa everytime I asked but seemed like after 2 days he forgot it and just chilled out. Obviously he couldnt travel and do almost nothing.
When he had to go back his country he had to fix his visa, there was no agency able to deal with expired visas and specially that long expired.
He got some lawyer and went with him to Entry & exit bureau, he got a penalty around 15k rmb and got a 10 day visa with no possibility to be renewed anywhere. That was stated in the visa coz I saw it, it had a note saying the holder must return to his country of origin.

Let me tell you first that in order o get a new visa placed in your existing passport, the passport CAN NOT expire for at least 6 months.  It is clearly written in the regulations for new Chinese visas.

I had the same problem in Guangzhou in 2009 when my daughter's passport expired.  After researchng, found out that to just renew the passport, the Consulate had a 45 days wait to get an appointment, makes no difference if expired or not.  But if I claimed it was stolen, I walk in, no wait, and get a new one withing 14 days.

So, I went to local Police and filed a claim that her passport was stolen, showing a photocopy of all the passport.  They gave me a paper with a case number, and with it went to PSB in Guangzhou, who gave inmediately a 30 days visa for my daughter to stay in China and attend her school.

Then went to Consulate and requested a new passport, showing all the paperwork accumulated so far.  Got new passport back in 14 days, pick it up and then went with daughter to HKG one morning early and got her a new student visa, went back to HKG and to PSB and they gave her a new residence permit.

The only draw back in doing this is that she was already on a two year renewal, and got pushed back to 6 months only.  But on the second one she got one year, and now she is back at two. 

It worked for me, I have no idea if it will work for you.

Now, I do not advise you to overstay your visa.  The fine is 500 Rmb per day.  But overstaying is consider by Chinese Officials as a very serious offense, for them it shows you have no respect for their Laws and Regulations, and could lead to deportation and denials of future visas sometimes. 

My advise, go to PSB with someone fluent in Chinese, and ask for a 30 days grace period to receive your new passport.  Show that you have already requested it, and hope for the best.  Otherwise, it would be wiser to leave China before visa and passport expiration date, and wait for new passport in HKG.

I took your advice HappyExpat and went with a teacher to the PSB. Boy, got tow completely different answers. The first person said that if I don't leave China before my visa expires, the police might even come after me and lock me up. Even if my new passport was to arrive one day after my expired visa, that could happen and said I would not get my visa renewed.
When we were leaving, my teacher came across one of his friends there and she said that as long as I don't overstay for too long, it's not that severe but in any case I would be able to get an extension.

Am freaking out right now as to who to believe...

Was considering the option of "hiding out" in HK , but read that your passport needs to be valid for at least a month? True or false?

And in case I have to leave, will I still be able to go to HK airport from the mainland with my (really) soon to be expired passport? Even if it's just to catch a flight on the same day?

It is hard for me to give you good advise because many details are unknown.  When you went to PSB, did you asl for your visa extension for 30 days?  Was it refused?

Can you go to local Police and claim your passport was stolen, then with their report go to PSB and they will give you a 30 days stay permit to get a new passport, then a departure permit and go to HKG to get a new visa?.  All of that is legal.

Or, do you have anyone you can trust and arrange for that person to pick your passport at Emabssy when it arrives and forward it to you in Hong Kong?.  Will the Embassy give your passport to a trusted friend if you request it?

You must find answers to all these questions before you decide what to do

You must have a vaild passport for 6 months for travelling almost anywhere. I will say this, I had a friend whose passport expired for 6 months. He got by with a slap on the wrist and this was during the 2008 olympics. It aslo helped that he had a person with some connections.

Your gonna have to do what I saw these two girls doing at the embassy. Begging for your life pleading your case and then calling home frequently to see if anybody there may assist you if things get out of hand. Sorry if I'm making you nervous, but I've seen it happen to these two girls that were standing in front of me. Getting loud won't help as they will say: "it is your fault, I'm here to take your money." -Sorry truth hurts sometimes!