This may or may not bring up the Corizine episode but I have a question and Corizine may have nothing to do with my question

Let's say I am a small investor with a portfolio of 100 shares of 5 different stks [number is not important to my question]

Now I don't have a certificate of ownership but I get a statement every so often telling me the total worth, usually individual stock value for that one Co. and any dividend paid. Statement are for just one Co. and come any time. We can also go online to look up our shares and other info at any time.

In our situation we usually seem to get a statement when dividends are paid, or qtrly.

Now do we actually own the stock if the brokerage goes broke. 

Do we have rock solid ownership of those stks.  In the old days we used to have stk certificates.

Also how can a brokerage or anybody lend  out shares unless they  own the stk

Are they lending my stks and collecting a fee

I know several people on the forum have stks so can you tell me if I have rock solid ownership of my stks and if somebody is selling, lending stks, whose stks are they selling, lending. 

Are they selling paper or real stks given the short position was 140% off that Co.[name if forget]