I don't think that would work. I'm presenting my understanding of things. Please chime in to correct me where I am off.
Let's start with a simple example. A company has a single class of shares. All these shares are fungible. This means that it does not matter that you hold share number 545 our of 1,000,000 or share number 390,056 out of a million. Each of these million shares is identical to the others. Just the same way each $1 bill is identical to each other $1 bill.
A stock split happens. Now there are twice as many shares. However, at the moment of the split, each share is worth half as much. The total market value has not changed. Of course, trading continues and the shares will move up or down in value.
Short holders will need to come up with 1 additional share for each 1 share that they hold. This is because the stock split affects the exact class of shares that the short holder owe.
If a company issues more shares of the same class, short sellers do not need to do anything. Nothing happened to their shares. I would imagine that the value of each outstanding share would drop, and short sellers would actually profit.
If the company issued shares of another class, that would not introduce new responsibilities to short holders.
Short holders are obliged to do things on shares that they actually own. A dividend affects existing shares, hence short sellers need to pay those dividends. A split affects existing shares, hence short sellers need to find extra shares to make the lender whole. A new stock issue does not affect those existing shares: new shares are being introduced.
Another way to think about this is to think what happens if you are long 1 share of a company. If a dividend is paid, then you are paid 1 share's worth of a dividend. If a split happens, your 1 share is now 2 shares (each at half the price of the original). However, if a company issues more stock, you do not get more shares. The same rules govern short sellers. However, they must give instead of receiving.